Random Variable Example(2)

let us say we are flipping a coin and p is the probability of getting head and (1-p) is the probability of getting a tail and N is a random variable that counts the number of times coin is flipped until we get first time head.

What is the probability of getting first time head in the fourth flip?

Answer

With this question, we will understand the important concept of random variables. 

The possible values that N can have are {1,2,3,4,5,6......} Why?

If we get Head as we flip first time then N=1

If we get head on the second flip then N= 2

If we get head on the third flip then N= 3 and so on

We can assign probability as:

P(N=1) = {H} = p

P(N=2)={TH} = (p-1)p

P(N=3) = {TTH}= (p-1)(p-1)(p)

P(N=4)={TTTH} =(p-1)(p-1)(p-1)(p)  // because getting head or tail is independent event so we can directly write it like this.

 

 

 

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