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.
Write out a formula for the probability distribution of the
random variable n. (Enter a mathematical
Compute the probabilities that n = 1, n = 2,
and n = 3. (For each answer, enter a number. Round your
answers to three decimal places.)
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
This is the pdf of the geometric distribution , i.e.
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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