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A. Find the probability that there is exactly two cars and exactly one bus during a trip? B. What is the probability that there is almost one car and at most one bus during a trip? C. What is the probability that there is exactly one car during a trip? Exactly one bus?

A. Find the probability that there is exactly two cars and exactly one bus during a trip? B. What is the probability that there is almost one car and at most one bus during a trip? C. What is the probability that there is exactly one car during a trip? Exactly one bus?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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Round off your final answer to four decimal places. Indicate units

Consider a ferry that can carry both buses and cars across a waterway. Each trip costs the owner approximately $12. The fee for cars is $2 and the fee for buses is $7. Let X and Y denote the number of buses and cars, respectively, carried on a given trip. The joint distribution of X and Y is given by YIX 1 2 0.01 0.03 0.01 1 0.03 0.07 0.08 Y 0.03 0.06 0.06 3 0.07 0.13 0.07 4 0.12 0.03 0.04 0.08 0.02 0.06 A. Find the probability that there is exactly two cars and exactly one bus during a trip? B. What is the probability that there is almost one car and at most one bus during a trip? C. What is the probability that there is exactly one car during a trip? Exactly one bus? D. Find E(X), E(Y), Var(X), Var(Y), o(x), o(y), marginal density for x and y E. Are X and Y independent, show your solution F. Find the correlation between X and Y variable and interpret your findings, show your solution.
Transcribed Image Text:Consider a ferry that can carry both buses and cars across a waterway. Each trip costs the owner approximately $12. The fee for cars is $2 and the fee for buses is $7. Let X and Y denote the number of buses and cars, respectively, carried on a given trip. The joint distribution of X and Y is given by YIX 1 2 0.01 0.03 0.01 1 0.03 0.07 0.08 Y 0.03 0.06 0.06 3 0.07 0.13 0.07 4 0.12 0.03 0.04 0.08 0.02 0.06 A. Find the probability that there is exactly two cars and exactly one bus during a trip? B. What is the probability that there is almost one car and at most one bus during a trip? C. What is the probability that there is exactly one car during a trip? Exactly one bus? D. Find E(X), E(Y), Var(X), Var(Y), o(x), o(y), marginal density for x and y E. Are X and Y independent, show your solution F. Find the correlation between X and Y variable and interpret your findings, show your solution.
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