Random Variable Introduction(1)

Before going into details let's know some basics about random variable:-

1. It is not random.

2. It is not a variable, it is a function.

3. The value of a random variable is determined by the outcome of the experiment.

A random variable is a function that takes the event of sample space and gives us some number. See, we are not Interested in knowing the exact experiment rather we are interested in knowing some number that defines that experiment.

Suppose we are rolling two dice and I want to know how many times we have values on dice such that their sum is 7 ??

Here we are not interested in knowing such samples like {(2,5), (3,4), (5,2), (1,6), (6,1) ,(4,3) , } . We just want to know a number.  let say Y is a function that counts our values 

So Y = 6  // it means out of total sample space that is formed by rolling a dice  6 values has 7 as a sum.

now if we assign a probability to them P(Y)= 6/36=1/6, It means with 1/6 probability we can have two values such that their sum is 7.


Example 1: let say we are flipping two coins and we are interested in knowing how many times head appears. Assume Y is a random variable that counts the number of head in this experiment.

Possible values that Y can take is {0,1,2} Why??

because when you toss 2 coins head may appears 0 time or 1 time or 2 time. If you assign a probability to random variables it is called probability distribution.

Now we can write it as

P(Y=0) = {TT} = 1/4 // it means what is the probabilty that 0 head appears .

P(Y=1) ={HT,TH} = 2/4 = 1/2

P(Y=2) = {HH} = 1/4

We will see more example to get more idea about Random Variables.