Question

On the leeward side of the island of Oahu, in a small village, about 88% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a)

Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.)
P(n) =

(b)

Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.)
P(1) =  
P(2) =  
P(3) =

Answer 1

Let X be a random variable which denotes the number of failures before the first success. By definition X follows geometric distribution with parameter p, where p is the probability of success.

Here the success is meeting the person of Hawaiian ancestry in the village where 88% of the residents are Hawaiian. So here p=0.88

(a)

This is the pdf of the geometric distribution , i.e.

i.e.

(b)

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.