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.

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