Question

1. Suppose a random variable X has a pmf 
p(x) = 3^(x-1)/4^x , x = 1,2,......

1. Suppose a random variable X has a pmf

p(x) = 3^(x-1)/4^x , x = 1,2,...
(a) Find the moment generating function of X. 

(b) Give a realistic example of an experiment that this random variable can be defined from its sample space. 

(c) Find the mean and variance of X.
Math   Statistics-And-Probability   
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Answer #1

Realistic example:

A company tests the manufactured bulbs until the first defective bulb is found. So the number of bulbs tested will be a geometric random variable taking values 1,2,3...

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