91Ó°ÊÓ

A coin is tossed repeatedly until a head is obtained for the first time

Let X denote the number of tosses that are required to get the first head

Let p be the probability of getting a head and q be the probability of getting a tail

The probability mass function of X will be

f(x) = q^x-1p where x=1,2,3…

CDF is given by

F(1) = p

F(2) = p +pq

F(3) = p +pq+pq²

F(4) = p+pq+pq² +pq³

And soon

If the coin is a fair coin, then

p=1/2

q=1/2

F(1) = 0.5

F(2) = 0.75

F(3) =0.875

And so on.

X axis of the graph contains the random variables and y axis contains its corresponding CDF value. For example, for random variable X=1 corresponding CDF valueF(1) = 0.5

Thus, plotting the Xvalues on the x-axis and their corresponding CDF on the y-axis,

the CDF curve is given by