 # Statistics for IT– Worldwideasy – 09

Statistics for IT– Worldwideasy – 09 to you today Demonstrate knowledge of Random Variable Definition.

## What Is a Statistics Random Variable?

A random variable is a variable whose function is unknown or assigned a value Value ​​for each test result. Random variables are often
Are named alphabetically and can be classified as variables.
Specific values ​​or variables are variables that can have any value
In a continuous range.

Random variables are often used in econometric or regression analysis. Determine the statistical relationships between each other

## Explaining Random Variables Statistics

In probability and statistics, random variables are used to quantify the return of a Coincidence, so many values ​​are available. Random variables Should be measured and are usually real numbers. For example, The letter X can then be named to represent the sum of the named numbers Three dice are rolled. In this case, it could be X 3 (1 + 1 + 1), 18 (6 + 6 + 6), or Somewhere between 3 and 18, the highest death toll is 6 and The minimum value is 1.

A random variable is different from an algebraic variable. Variable a
The algebraic equation is an unknown value that can be calculated. 10+ Equation x = 13 indicates that the exact value for x can be calculated as 3. On the other hand Hand, a random variable has a set of values, which can be any of those values Its repercussions can be seen in the example of the dice above.

In the corporate world, random variables can be assigned to properties such as the average price of an asset over a given period, the return on an investment after a specified number of years, the estimated turnover rate at a company within the following six months, etc. Risk analysts assign random variables to risk models when they want to estimate the probability of an adverse event occurring. These variables are presented using tools such as scenario and sensitivity analysis tables which risk managers use to make decisions concerning risk mitigation.

## Types Statistics of Random Variables

Statistics random variable can be discrete or continuous.

A significant number of discrete random variables take on different values. Consider an experiment in which a coin is tossed three times. If X represents The number of times the coin lands on the head, then X is a discrete random variable It can have only 0, 1, 2, 3 values ​​(without the succession coin three heads Throws to all heads). No other value can be set for X.

Continuous random variables can represent any value within a specific range Or an infinite number of gaps and possible values ​​can be obtained. The continuous random variable is a measurement-related test The amount of rainfall in a city over a year or the average height of a random group of 25 people.

If y represents the random variable for the average height, draw on the second In a random group of 25 people. The results are a
Since the height can be 5 feet or 5.01 feet or 5.0001 feet, there is a continuous number of infinite number of possible values ​​for height.

## Finally

Statistics random variable has a probability distribution probability That any possible value can occur. The random variable Z is the number on the upper face of the deceased when it is rolled once. Possible values
For Z will be 1, 2, 3, 4, 5, and 6. The probability of each of these values ​​is 1/6 Because they can all be equal in value to Z

For example, the probability of getting 3, or P (Z = 3) at death is 1/6,
So is the probability that all six faces have 4 or 2 or some other number To die. Note that the sum of all probabilities is 1.

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Statistics for IT– Worldwideasy – 08 to you today Demonstrate knowledge of Continuous Random Variables.

If a random variable is possible, it is continuous Assume an infinite number of values Correspond to the points of a linear gap.

## Continuous Probability Distribution

Suppose we measure the height of the students in this class. If we
“Discrete” to the nearest feet, to the discrete The probability histogram is shown on the left. If tall now Measured to the nearest inch, the probability is a histogram Shown in the middle. We get more pots and smoother the appearance. Suppose we proceed in this way to measure height More and more subtly, probabilistic histograms as its counterpart Enter a smooth curve shown on the right.

### Probability Distribution for a ContinuousRandom Variable

The probability distribution describes how probability exists Distributed on all possible values. the probability distribution for Continuous random variables are determined by x arithmetic The function denoted by f (x) is called the dens function. The graph of a function is a smooth curve.

## The Normal Distribution

The Statistics generating formula Average probability distribution:

Two parameters, mean and standard deviation, Determine the average distribution completely. The shape and location of the average curve are very Difference between mean and standard deviation.

## Using Table 3 – Statistics

The probability of four digits in a particular row and column Table 3 gives the area under the standard average The curve between 0 and the positive value is z. This is enough Since the standard average curve is symmetric

• Read on to find an area between …. 0 and the positive z value Straight from the table.
• Use the properties of the standard average curve Probability laws for finding other fields.

## Working Backwards Statistics

Most of the time we know the area and want to find the z value It gives the area. Example: Find the value of positive z with an area Between 47750 0 and z.

### The Normal Approximation to theBinomial

We can calculate binary probabilities

• Binary formula Cumulative binary tables When n is large, and when p is not close to zero One, areas with mean np under the normal curve And variability npq can be used approximately Binary probabilities.

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Statistics for IT– Worldwideasy – 07 to you today Demonstrate knowledge of statistical applications. Distinguish between the two branches of statistics. Identify data types. Identify the measurement level for each variable. Takes discrete random variables Only a limited or countable number. Values. There are a few useful abstractions. These can be learned.

## The Binomial Random Variable

Coin tossing experiment A simple example for binary Random variable. Throw a fair coin
n = Record 3 times and x = count Empty.

Many situations in real life are like a coin. The advantage of the coin, but the coin is not necessarily fair.

## Cumulative Probability Tables – Statistics

You can use cumulative probability tables. To find the probabilities for the selected binary and To distribute.

## The Poisson Random Variable

Poison random variables x is often a model. For data representing numbers Events of a specific event in a given unit In time or space.

• A number of calls received during a specified period.
• The number of machine breakdowns per day.
• A number of road accidents given Within a certain period of time.

You can use cumulative probability tables. The probabilities for the selected poison must be found.

## The Poisson Probability Distribution

According to probability theory and statistics, the Poisson distribution French pronunciation, named after the French mathematician Simon Denis Poison, is a discrete probability distribution that expresses the probability of a certain number of events. If these events occur at a known constant mean ratio and independently of the time after the final event, then the time or space gap.  Poison distribution can also be used for many events over other specific time periods, such as distance, area, or volume.

## Key Concepts – Statistics

• Five features: n Similar experiments, each line Success S or Failure F, Probability of success p and From trial to trial is constant; Experiments are independent. x is the number of successes of n experiments.
• The number of events that occur over a period of time or Space, events, in general, expect such events.
• The number of successes in a finite to n-sized sample Populations with M successes and N-M failures.

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Statistics, Nothing in life is guaranteed to you in this part We are in everything we do Opportunities to get successful results from business medicine to weather provides a quantitative description of probability. It provides a bridge between description and conjecture Statistics.

## Probabilistic vs Statistical Reasoning

Suppose I know the exact car ratio in California. Then I can find probably the first car I see on the street A Ford. This is probabilistic logic like mine. Know the population and predict the sample. Now suppose I do not know The rate of car production in California, though I would like to evaluate them. I’m watching Random car samples on the road and then There is an estimate of the proportions. This is statistical logic.

## What is Probability?

• We used charts and numerical measurements. Describe the typical sample datasets.
• We used charts and numerical measurements. Describe the typical sample datasets.
• An experiment is a process that Gets observations.
• An event is the result of an investigation, Usually in capital letters.

## Statistics – Experiments and Events

• If two events are reciprocal, when One event happens, the other cannot and vice versa On the other hand.
• Called an indestructible event A simple event.
• Indicated by e with a contribution.
• Every simple event is assigned Probability, measuring the number of times it occurs.
• A set of all the simple cases of an experiment Called the sample space, s.

## The Probability of an Event

• A set of all the simple cases of an experiment Called the sample space, s.
• If we let n get infinitely large,

## Statistics – Counting Rules

• There are 216 inclusions in the sample space for throwing 3 dice, the sample space There are 1296 inclusions for throwing 4 dice,
• At some point, we should stop listing and start thinking.
• We need some rules of calculation.
• If the experiment is done in two stages, With m method to complete the first stage and Ways to complete the second stage There are mn ways to accomplish that Should be tried.

## Event Relations

The beauty of using events instead of simple ones We can combine events and use other events. Logical operations and, or not. That is the sum of the two events A and B. A or B or both occur when the experiment takes place Was done.

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Statistics for that. Here you have, Applying the basic calculation principle. Calculation of percussion. Calculation of Comb Combinations. Distinguish combinations against per induction. Can be done.

## Fundamental CountingPrinciple -Statistics

Can be used here Determine the number of possible consequences
When there are two or more symptoms. and Can be used here Determine the number of possible consequences When there are two or more symptoms.

Motivation is a provision. In a specific order.

## Permutations – Statistics

To find the number of triggers here Items, we can use basic. By the principle of calculation or by factorial notation.

## Combinations

Is a combination of Items not ordered are a material arrangement.

Because the order is not important Combinations, there are fewer combinations. Than inductions. Combinations A “subset” of triggers.

In mathematics, a combination is a selection of items from a collection, the order of selection is not important (unlike inductions). For example, give three fruits and say one apple, one orange, and one pear, three combinations of two can be extracted from this set: apple and pear Apples and oranges; Or pears and oranges. More formally, the k-combination in an S set is a subset of the k-specific elements in S. If the set has the element n, the number of k-combinations is equal to the two-dimensional coefficient.

See the below examples and get the idea,

Next, we meet with a very wide-ranging lesson. Until then, keep these lessons in mind.

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Statistics for that. Expansion Summarize data using median trend measurements such as the mean. Mean, mode, and midrange. Describe data using variability measurements such as range, variability, and so on. Identify the location of a data value in a dataset using various measurements, such as percentages, decimals, and quarters in Statistics.

## Measures in Statistics

### Measures in Central Tendency in Statistics

• A measure of centripetal tendency is a detailed statistic. Describes the average or average value of a set of points.
• There are three common measures of central tendency,
• mean
• median
• mode
• When raw data is organized it helps to display it. The form of a table showing the frequency (e) with each data Item (x) occurs. Such a table is called a frequency table.
• However, this may be the case when a large range of data is involved. Breaking down data into smaller groups first is beneficial. In which case, the resulting table is called a group Frequency table.

### Mean (Arithmetic Mean)

• The average calculation of mean numbers “middle” Is the value of a set of numbers. Add up all the numbers to calculate it. Then divide how There are many numbers.
• The arithmetic mean or abbreviated mean of an N group.

#### THE ARITHMETIC MEAN COMPUTED FROMGROUPED DATA IN STATISTICS

Assumes a procedure for finding the mean for group data. That the mean of all raw data values ​​in each class is the same Takes the middle point of the class. In reality, this is not true. The average of the raw data values ​​for each class will not be average. The same as the midpoint. However, using this procedure From some Will give an acceptable approximation of the mean.
Values ​​fall above the midpoint and other values ​​fall below For each class, the midpoint and the midpoint represent Assessing all values ​​in the class.

Ex: Miles Run per Week

### The Median

The mean is half of a dataset. Before you can find this out, the data must be arranged in order. Then The dataset is ordered, which is called the data array. Mean Will fall between a certain value or two in the dataset.

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Statistics for it. Expanding the amount given in Sigma notation to a clear amount through this statistics lesson. Write a clear sum of S sigma notation. A clear pattern for individual terms. Using rules to handle money is expressed in Ig sigma notation. Explained.

## Sigma Notation for Statistics

• Sigma notation is a method used to write a long sum in a Short path.
• For example, we often like to summarize a number of terms 1 + 2 + 3 + 4 + 5 or a 1 + 4 + 9 + 16 + 25 + 36 There is a clear pattern to the numbers.
• More generally, we have u1, u2, u3,. . . , Otherwise we can write the sum of these numbers as u1 + u2 + u3 +. . . + un.
• This is an abbreviated form of writing that allows ur to represent the general term and put it in sequence.

See the Below example forget some idea.

## Writing a long sum in sigma notation – Statistics

Statistics – We have been given a long sum of money and suppose we want to declare. It is from Sigma numbering. How should we do this?

See below example,

## Rules for use with sigma notation

• In general, we can write if we add a constant n time.
• Suppose we have a fixed time collection.
• But from this calculation, we can see that the result is the same.
• Suppose we have the sum of k and a constant. Give us this.
• But from this calculation, we can see that the result is the same.
• If a and c are constants, and f (k) and g (k) are the functions of k.

See the below example for more knowledge,

I hope you have gained a great deal of knowledge from this section. Stay with us often so you can gain a very broad knowledge. See you soon in another lesson!

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Through this Statistics lesson, you Identifying different types of data, Describing the data presented as a list, Describing the discrete data presented in a table, Describe continuous data presented by a group frequency.

##### RAW DATA

Data that does not collect raw data is collected
Statistically organized.

##### ARRAYS

An array is a set of raw number data
The order of ascent or descent of magnitude.

#### Range

The biggest and the difference between
The smallest number is called the range
Data.

#### Data

The first step is to summarize the quantitative data
To determine whether the data is discrete
Continuous.

### Discrete data – Frequency Table

A frequency table is arranging in order. The collected data are in chronological order. Their magnitude is a relative frequency.

### Grouped frequency table

• Class gap – A symbol that defines a class of 60-62 The given table is called the class interval.
• Class Limits – The end numbers, 60 and 62, are called class limits the smaller number (60) is the lower class limit, and the larger number (62) is the upper-class limit.
• Open Class Intervals – A class interval that, at least theoretically, has either
no upper-class limit or no lower class limit indicated is called an open class interval.
• Class Boundaries – If heights are recorded to the nearest inch, the class interval 60–62 theoretically includes all measurements from 59.5000 to 62.5000 in. These numbers, 59.5 and 62.5, are called class boundaries, the smaller number (59.5) is the lower class boundary and the larger number
(62.5) is the upper-class boundary.
• The size, or width, of a class gap – The size or width of a class gap The difference between lower and upper class Is the boundary and is also known as the class Width, class size or class length.If all class intervals in a frequency distribution. Of equal width, this common width is indicated
C. In such a case c is equal to the difference Between two or two successful lower class boundaries Successful upper class boundaries.
• Classmark – The classmark is the midpoint of the class gap Obtained by adding bottom and top Class boundaries and division by 2.

### The Frequency Polygon

If another way to represent the same dataset Using a frequency polymer.
A graph showing the frequency polymer Data using points connecting lines
Designed for frequencies at midpoints of. Classes. Frequencies represented score.

### The Ogive

Ogive is a graph that represents. Cumulative frequencies for classes
There is a frequency distribution.

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Today we hope to focus on a different topic. This is very important for people who are educated. Statistics for it is the topic here. Let’s find out now.

## Introduction to Statistics

Collection science, organization, presentation, analysis and
Interpret data to assist in making more effective decisions and Used to summarize and analyze statistical analysis.
The data is then processed into useful decision-making information

## Types of statistics

• Detailed Statistics – Methods of Organizing, Summarizing, and Presenting data in an informative manner.
• Guessing Statistics – Methods used to determine something About a population on a sample basis.

## Inferential Statistics

• Estimation
• Hypothesis testing

## Sampling

A sample should have similar characteristics
As the population it represents.

Sampling methods can be :

• random
• nonrandom

Random sampling methods,

• Simple random sample
• Stratified sample
• Cluster sample
• Systematic sample

Descriptive Statistics,

1. Collect data
2. Present data
3. Summarize data

#### Statistical data

• Collect data relevant to the problem being studied. This usually the most difficult, expensive, and time-consuming part.
• Statistical data are usually obtained by counting or measuring items.
• The variable is an item of interest that can be taken in a variety of ways Numerical values.
• A constant has a fixed numeric value.

### Data Collection Methods

• Interviews
• Questionnaires
• Survey
• Observation

• Qualitative
• Quantitative

## Qualitative Data

Quality data is usually described in words Letters. They are not as widely used as quantitative data This is because most numerical techniques do not apply Quality data. For example, it makes no sense to Find a normal hair color or blood type.

## Quantitative Data

Quantitative data are always numbers and they are Results of calculating or measuring the characteristics of a population. this data can be divided into two Subgroups:

• Discrete
• Continuous

## Types of variables

The numerical scale of measurement

• Nominal
• Ordinal
• Interval
• Ratio

## Data presentation

This has used 6 methods for data presentation.

• Histogram
• Frequency polygon
• Ogive
• Pie Chart
• Bar chart
• Time Series Graph

#### Histogram

Graphically used frequently. Current time interval and rate data Often used interval and Rate data. Shown from adjacent bars There are a numerical range In summary Arbitrarily selected frequencies Class values.

#### Frequency polygon

Another common method is The gap presented graphically And rate data.
To create a frequency Marks the frequency of the polymer On the vertical axis and Values ​​of variability Measured on the horizontal axis, Like a histogram. If the purpose of the presentation Comparing with others Distribution, frequency The polygon provides a good stuff Summary of data.

#### Ogive

A graph of a cumulative Frequency distribution. For a relative frequency, This can be used to turn.

#### Pie Chart

Pie note is an effective method. Percentage display Divides data by category. Relative sizes are useful. The data must be components.

#### Bar chart

Nominal submission And average scale data. Uses one column to represent Frequency for each category. The bars are usually positioned With their base vertically Located on the horizontal axis.

#### Time Series Graph

Time series graph It is a data graph measured over time. The horizontal axis here This graph represents Time limits and Shows the vertical axis Numerical values Corresponds. # Ruby Course – Worldwideasy – 04

Ruby lesson 4. I will focus on Getting Control Statements (IF statement, Case Expressions, loops), Comments, and File Control. It can provide extensive knowledge.

## Control Statements

A control statement is a statement that determines whether other statements are active. If a statement decides whether another statement should be executed, or one of the two statements to be executed. A loop determines the number of times another expression should be executed.

Basically have 3 control statement

• IF
• Switch
• Loops

### IF Statement in Ruby

If a statement is used to check the condition, it can be a condition or more. The special feature of it is that you can check any gap. The following example will make it clear to you.

``````ismale = false
if ismale
puts "you are male"
else
puts "you are not male"
end``````

This Code output is you are not male.

### Case Expressions

The Case Expressions is used to check several non-gap conditions. This works very fast and gets the idea below

``````def get_day_name(day)
day_name=" "

case day
when "mon"
day_name = "Monday"
when "tue"
day_name = "Tuesday"
when "wed"
day_name = "Wednesday"
when "tur"
day_name = "Thursday"
when "fri"
day_name = "Friday"
when "sat"
day_name = "Saturday"
when "sun"
day_name = "Sunday"
else
day_name = "Invalid"
end
return day_name
end
puts get_day_name("wed")``````

This code output is Wednesday.

## Loops

Loops have main 3 loops in php

• For loop
• While loop

Now I show the First 3 loops using Code. See Below all code output is the same. output is : 1,2,3,4,5,6,7,8,9,10.

#### For Loop with Arry

``````num = [1,2,3,4,5,6,7,8,9,10]
for num in num
puts num
end``````

#### While Loop

``````index = 1
while index < 8
puts index
index + = 1
end``````

## Ruby Comment

Comments are a special character in programming.

``````# single line comment
= multiline
comment =``````

## File Control using Ruby

Here we show you how to handle files without opening them. see below

``````file.open("test.txt",r) do |tile|
end``````
##### Write File
``````File.open("employee.txt","a") do |file|
file.write ("sanka")
end``````
##### Create File
``````File.open ("index.html","w") do |file|
file.write("<h1>Hello</h1>")
end``````
``````File.open ("employee.txt","rt") do |file|
file.write ("overridden")
end``````

## Class & Object

Class is collection of objects and functions. In computer programming, a function object is a construct that allows an object with the same syntax to be called or called a normal function. Active objects are often referred to as funksters.

This is the mining of the object and class. now we can try to add it ruby. look below example.

``````class Book
attr_accessor :title, :author, :pages
end

book1 = Book.new()
book1.title = "Harry Potter"
book1.auther = "JK"
book1.pages = 400
puts book1.pages``````

Output is 4000.

## Method

See the below example. that use code reuses it easy for developing softwares.

``````Class
attr_accessor:name, :major, :gpa
def initialize (name,major,gpa)
@ name = name
@ major = major
@ gpa = gpa
end
end
student1 = student.new ("harry","bio","3.6")
student2 = student.new ("jhone","chem","2.1")

puts.student1.name``````

Output is harried.

## Create a Ruby 2D Game

First, install ruby 2d gem. open cmd

``gem install ruby2d``