Answered: Suppose that the random variables X and…

Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2),

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 16E

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Question

Suppose that the random variables X and Y have a joint density function given by:

f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise

Find the constant c,
P(Y≥1/2),
P(X < 2, Y >1/2),
P(X < 1),
Determine whether X and Y are independent.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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