Question: Suppose that joint probability density function (pdf) of A and B is given by f A,B ( a,b ) = k(a-b), if 0

Suppose that joint probability density function (pdf) of A and B is given by fA,B(a,b) =k(a-b),if 0<=y<=x<=1, andfA,B(a,b) = 0 otherwise.

a. Show that k = 6 in order for the above fA'B(a,b) to be a valid pdf.

b. Derive the marginal pdf of B.

c. Derive the conditional pdf of B given A =a, where 0<=a<=1.

d. Find P(A+B <= 1).

e. Derive the pdf of C = A + B.

For best answer please show work.

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