Please answer i,ii,iii, and show steps if possible. Do not randomly write wrong answers if don't know how to solve. Solve the following questions:1) Let X & Y have the joint probability function f(x, y) = k(1-xy), 0≤x≤ 1,0 ≤ y ≤ 1.i) Find k such that this is a proper probability function.ii) Find the marginal probability, expectation and variance of X and Y.iii) Find E(X+Y).

Answered: Image /qna-images/answer/59f94818-29f9-4e0f-82a7-5cdcdd9dd3a2.jpg

Answered: Solve the following questions: 1) Let X…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 33E

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Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious problem in hemlock trees. Researchers have developed the following function that estimates the probability P that a given hemlock tree has ring shake: P(A,B,D)=11+e3.680.016A0.77B0.12D where A is the age of the tree yr, B is 1 if bird pecking is present and 0 otherwise, and D is the diameter in. of the tree at breast height. Source: Forest Products Journal. a. Estimate the probability that a 150-year-old tree with bird pecking present and a breast height diameter of 20in., will have ring shake. b. Estimate the probability that a 150-year-old tree, with no presence of bird pecking and a breast height diameter of 20in., will have ring shake. c. Develop a statement about what can be said about the influence have on the probability of ring shake. d. Using the total differential, estimate the probability if the actual age of the tree was 160 years and the diameter at breast height was 25in., Assume that no bird pecking was present. Compare your answer to the actual value. Hint: Assume that B=0 and exclude that variable from your calculations e. Comment on the practicality of using differentials in part d.

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Solve the following questions: 1) Let X & Y have the joint probability function f(x, y) = k(1-xy), 0≤x≤ 1,0 ≤ y ≤ 1. i) Find k such that this is a proper probability function. ii) Find the marginal probability, expectation and variance of X and Y. iii) Find E(X+Y).