Question

Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 75% 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) = p(1-2)^n-1 (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) = 0.75 P(2) = 0.188 P(3) = 0.047 (c) Compute the probability that n > 4. Hint: P(n = 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.016 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use u for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents Need Help? Read It Talk to a Tutor

On the leeward side of the island of Oahu, in a small village, about 75% 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.)

Answer 1

solution - Given data : het x denotes the first person village the of number of Hawailan people entil encounter ancestry in the - 75% of the residends are ob Hawailan ancestoy so P 79co.75 ! Let n= 1,2,3,---ri Here we find the footala for the probability distribution in Mathematically, US A probability distribution of randon varitable 'n'hi 0.75 (1-0-775)" TPCN) = 0.15 (0125) y Here we find expected norber > E(X) =é et = 1.333271.. 0.75 whole norool i 1 sesidents. 1.