A stock solution of hydrochloric acid (HCl) supplied by a certain vendor contains small amounts of several impurities, including copper and nickel. Let X denote the amount of copper and let Y denote the amount of nickel, in parts per ten million, in a randomly selected bottle of solution. Assume that the joint probability density function of X and Y is given by { S c(x + y) 0 < x < 1 and 0 < y < 1 f(x,y) = otherwise Find the value of the constant c so that f(x,y) is a joint density function. Compute the marginal density function fx(x). a. b. Compute the conditional density function fyx(y | x). C. d. Compute the conditional expectation E(Y | X = 0.4). Are X and Y independent? Explain. e.

A stock solution of hydrochloric acid (HCl) supplied by a certain vendor contains small amounts of several impurities, including copper and nickel. Let X denote the amount of copper and let Y denote the amount of nickel, in parts per ten million, in a randomly selected bottle of solution. Assume that the joint probability density function of X and Y is given by { S c(x + y) 0 < x < 1 and 0 < y < 1 f(x,y) = otherwise Find the value of the constant c so that f(x,y) is a joint density function. Compute the marginal density function fx(x). a. b. Compute the conditional density function fyx(y | x). C. d. Compute the conditional expectation E(Y | X = 0.4). Are X and Y independent? Explain. e.

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

Section13.3: Special Probability Density Functions

Problem 2E

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