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fx.x(1, y)= ce-r-5y if r, y20 otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fYix=z- (d) Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely 12ye-e-2y if z, y 20 Īxx(1, y) = - :- %3D otherwise (e) What is the probability P(Y² > 2X > 0) ?

fx.x(1, y)= ce-r-5y if r, y20 otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fYix=z- (d) Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely 12ye-e-2y if z, y 20 Īxx(1, y) = - :- %3D otherwise (e) What is the probability P(Y² > 2X > 0) ?

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 2YT
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Suppose that X and Y have a joint probability density function given by: 

 

( only for D) and E), ignored A),B)and C))

function given by ce-3r-5y if z, y 2 0 fx.x(1, y) = %3D otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fyx=z- (d) Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely Īxx(1, y) = < J 12 ye-3-2y² if z, y >0 otherwise (e) What is the probability P(Y² > 2X > 0) ?
Transcribed Image Text:function given by ce-3r-5y if z, y 2 0 fx.x(1, y) = %3D otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fyx=z- (d) Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely Īxx(1, y) = < J 12 ye-3-2y² if z, y >0 otherwise (e) What is the probability P(Y² > 2X > 0) ?
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