Let X and Y be random variables having joint density function [C 2x + y) Osxs1,0sys2 F(x,y) =10 otherwise a. What is the value of C? b. What is the probability that X is greater than % and Y is less than 3/2? c. Determine the marginal density function of X and Y. d. Find E(X) , E(), Var(X), Var(Y), σκ), , σί) e. Are X and Y independent, show your solution f. Find the correlation between X and Y variable and interpret your findings, show your

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Let X and Y be random variables having joint density function

a. What is the value of C?
b. What is the probability that X is greater than 1⁄2 and Y is less than 3/2?
c. Determine the marginal density function of X and Y.
d. Find E(X), E(Y), Var(X), Var(Y), σ(x), , σ(y)
e. Are X and Y independent, show your solution
f. Find the correlation between X and Y variable and interpret your findings, show your
solution.
g. Find the conditional density for X given Y=y, conditional density for Y given X=x

Let X and Y be random variables having joint density function
[C 2x + y)
Osxs1,0sys2
F(x,y) =10
otherwise
a. What is the value of C?
b. What is the probability that X is greater than % and Y is less than 3/2?
c. Determine the marginal density function of X and Y.
d. Find E(X) , E(), Var(X), Var(Y), σκ), , σί)
e. Are X and Y independent, show your solution
f. Find the correlation between X and Y variable and interpret your findings, show your
solution.
g. Find the conditional density for X given Y=y, conditional density for Y given X=x
Transcribed Image Text:Let X and Y be random variables having joint density function [C 2x + y) Osxs1,0sys2 F(x,y) =10 otherwise a. What is the value of C? b. What is the probability that X is greater than % and Y is less than 3/2? c. Determine the marginal density function of X and Y. d. Find E(X) , E(), Var(X), Var(Y), σκ), , σί) e. Are X and Y independent, show your solution f. Find the correlation between X and Y variable and interpret your findings, show your solution. g. Find the conditional density for X given Y=y, conditional density for Y given X=x
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