Before understanding the concept of random variables, you need to know what is a sample space in probability.

##

The range of all possible outcomes of an experiment is known as the 'Sample Space' (s).

Now let's understand the definition of Random Variables-

##

A random variable is a function which can take on any value from the sample space and having range of some set of real numbers, is known as the random variable of the experiment.

##

##

##

Random variables can be classified as-

#Discrete Random Variables and

#Continuous Random Variables

Now we will understand the Discrete Random Variables with the help of an example-

##

These are the random variable which can take on only finite number of values in a finite observation interval. So we can say that to discrete random variable has distinct values that can be counted.

We Will understand this with the help of an example-

##

Let's take an example (experiment) of tossing 3 coins at the same time (simultaneously).

Now for this experiment the sample space is

S= {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Here let's suppose that the number of tails is the random variable X

So X= {0 1 1 1 2 2 2 3}

= {x1 x2 x3 x4 x5 x6 x7 x8}

Now let's discuss other type of random variables i.e. Continuous random variables.

##

A random variable that takes on an infinite number of values is known as a continuous random variable. Many physical systems (experiments) can produce infinite number of outputs in a finite time of observation. In such cases we use continuous random variables to define outputs of such systems.

##

Example 1- A random variable that measures the time taken in completing a job, is continuous random variable, since there are infinite number of times (different times) to finish that job.

Example 2 - Noise voltage that is generated by an electronic amplifier has a continuous amplitude. Therefore sample space (S) and random variable (X) both are continuous.

##
__What is Sample Space in probability (S)__

The range of all possible outcomes of an experiment is known as the 'Sample Space' (s).__What is Sample Space in probability (S)__

Now let's understand the definition of Random Variables-

**ðŸŒ“**__READ THIS ALSO__:-**Probability Density Function (PDF) - Definition, Basics and Properties of Probability Density Function (PDF) with Derivation and Proof**##
__Random Variable (Random Variable Definition)__

A random variable is a function which can take on any value from the sample space and having range of some set of real numbers, is known as the random variable of the experiment.__Random Variable (Random Variable Definition)__

##
__Watch the Complete Video Here-__

__Watch the Complete Video Here-__

##
**Types of Random Variables**

Random variables can be classified as-**Types of Random Variables**

#Discrete Random Variables and

#Continuous Random Variables

Now we will understand the Discrete Random Variables with the help of an example-

##
**Discrete Random Variables**

These are the random variable which can take on only finite number of values in a finite observation interval. So we can say that to discrete random variable has distinct values that can be counted.**Discrete Random Variables**

We Will understand this with the help of an example-

**ðŸŒ“**__READ THIS ALSO__:-**Cumulative Distribution Function (CDF) - Properties of CDF - CDF Definition, Basics - Continuous and Discrete CDF**

##
__Example of Discrete Random Variable__

Let's take an example (experiment) of tossing 3 coins at the same time (simultaneously).__Example of Discrete Random Variable__

Now for this experiment the sample space is

S= {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Here let's suppose that the number of tails is the random variable X

So X= {0 1 1 1 2 2 2 3}

= {x1 x2 x3 x4 x5 x6 x7 x8}

Now let's discuss other type of random variables i.e. Continuous random variables.

##
__Continuous Random Variables__

A random variable that takes on an infinite number of values is known as a continuous random variable. Many physical systems (experiments) can produce infinite number of outputs in a finite time of observation. In such cases we use continuous random variables to define outputs of such systems.__Continuous Random Variables__

**ðŸŒ“**__READ THIS ALSO__:-**Joint Probability Density Function (Joint PDF) - Properties of Joint PDF with Derivation- Relation Between Probability and Joint PDF**

##
__Examples of Continuous Random Variables__

Example 1- A random variable that measures the time taken in completing a job, is continuous random variable, since there are infinite number of times (different times) to finish that job.__Examples of Continuous Random Variables__

Example 2 - Noise voltage that is generated by an electronic amplifier has a continuous amplitude. Therefore sample space (S) and random variable (X) both are continuous.

**Go to HOME Page**__Read More-__**Random Variables (Discrete and Continuous Random Variables), Sample space and Random Variables Examples****Probability Density Function (PDF) - Definition, Basics and Properties of Probability Density Function (PDF) with Derivation and Proof**
## No comments:

## Post a Comment