6)- Let x and y have the joint density f(x, y) = {* + cy if 15x< 2;0

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6) h and g. Solve them step by step.
6)- Let x and y have the joint density
f(x, y) = {* + cy if 15x< 2;0<ys1
elsewhere
where c is a constant
a) Find the value of c that makes f(x, y) a probability density function.
b) Find the marginal density for y and show that
O)dy = 1
c) Find f1(xly), the conditional density for x given y.
d) Find E(x)
e) Find E(y)
f) Find E(x + y)
g) Are x and y independent?
h) Find the covariance of the random variables x and y.
Transcribed Image Text:6)- Let x and y have the joint density f(x, y) = {* + cy if 15x< 2;0<ys1 elsewhere where c is a constant a) Find the value of c that makes f(x, y) a probability density function. b) Find the marginal density for y and show that O)dy = 1 c) Find f1(xly), the conditional density for x given y. d) Find E(x) e) Find E(y) f) Find E(x + y) g) Are x and y independent? h) Find the covariance of the random variables x and y.
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