Question 1 given by Suppose that X and Y have joint density function fx,y ce-2(x+y) if r>0 and y>0 otherwise fx,y (x, y) = (a) Show that fx,y is a valid probability density function if and only if c = 4. (b) Find the probability P(X < 2, Y < 3). (c) Find the marginal probability density function fx of X. (d) Calculate the conditional density function fy\X=x(Y). (e) Are X and Y independent? Are X² and Y4 independent? Justify your answers.

MATLAB: An Introduction with Applications
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Question 1-
given by
Suppose that X and Y have joint density function fx,y
if r>0 and y>0
otherwise
fx.y(x, y) =
ce-2(x+y)
0
(a) Show that fx,y is a valid probability density function if and only if c = 4.
(b) Find the probability P(X < 2, Y <3).
(c) Find the marginal probability density function fx of X.
(d) Calculate the conditional density function fyx=x(y).
(e) Are X and Y independent? Are X² and Y4 independent? Justify your answers.
Transcribed Image Text:Question 1- given by Suppose that X and Y have joint density function fx,y if r>0 and y>0 otherwise fx.y(x, y) = ce-2(x+y) 0 (a) Show that fx,y is a valid probability density function if and only if c = 4. (b) Find the probability P(X < 2, Y <3). (c) Find the marginal probability density function fx of X. (d) Calculate the conditional density function fyx=x(y). (e) Are X and Y independent? Are X² and Y4 independent? Justify your answers.
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