Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 00, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x
Suppose that the joint probability density
fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x
0, otherwise
Give your answers to the below questions in two decimal places where appropriate.
(a) The marginal probability density function of X is given by:
fX(x) = A xB e-3x , for 0<x<∞
0, otherwise
Find the value of A.
(b) Find the value of B.
(c)
The conditional probability density function of Y, given that X=x for some x>0, takes the following form:
fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x
0, otherwise.
Find the value of C
(d)Find the value of D.
(e)Find the value of E.
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