Problem 18E

use the result of 17 and table A.1 to find P(X=10)where X~Geom(0.3).

Solution :

Step 1 of 1:

Given, P(X=10) where Geo(0.3)

The formula of P(X=n) is

P(X=n)=

So XGeo(p) and

Here n=10 and p=0.3

Our goal is :

We need to find P(X=10) where Geo(0.3)

The formula of the geometric distribution is

P(X=10)=

Where q = (1-p)

So P(X=10)=

P(X=10)=

P(X=10)=

P(X=10)=

P(X=10)= 0.01210

Therefore the Geo(0.3) is 0.01210.

Then, P(X=10)=

The formula of the binomial distribution is

Here the probability of X is 10 and the probability of Y is 1.

P(X=10)=

P(X=10)=

P(X=10)=

P(X=10)= 0.1210

Therefore P(X=10) is 0.1210.