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Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤ y ≤1 elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y).

Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤ y ≤1 elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y).

Calculus For The Life Sciences
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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QUESTION 3 Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x, y) = = {k(x + y), 0≤x≤ y ≤1 elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y). d) the conditional pdf of Y given X. e) E(Y|X = -1)
Transcribed Image Text:QUESTION 3 Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x, y) = = {k(x + y), 0≤x≤ y ≤1 elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y). d) the conditional pdf of Y given X. e) E(Y|X = -1)
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