Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 84% 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) = (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.) (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 μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Use the geometric probability distribution to solve the following problem.
On the leeward side of the island of Oahu, in a small village, about 84% 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) =
(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.)(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 μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)residents
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