Probability & statistics

Use the geometric pro 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. P (n ) - | (b) Compute the probabilities that n = 1, n - 2, and n - 3. (Round your answers to three decimal places.) P(1 ) - P ( 2) P(3) - (c) Compute the probability that n 2 4. Hint: P(n = 4) - 1 - P(n - 1) - P(n - 2) - P(n - 3). ( Round your answer to three decimal places.) (d) In a more urban part of Oahu, it is estimated that about 8% of the residents are of Hawaiian ancestry. Repeat parts (a), (b), and (c) for this part of the island. (i) Write out a formula for the probability distribution of the random variable n. P ( n ) = (ii) Compute the probabilities that n = 1, n = 2, and n = 3. (Round your answers to three decimal places.) P(1) = P(2) - P (3 ) (iii) Compute the probability that n 2 4. Hint: P(n 2 4) = 1 - P(n = 1) - P(n - 2) - P(n - 3). (Round your answer to three decimal places.) 55#F O 12:06 PM Mostly sunny 10/4/2022 hp