We determined that f(y1, y2) = 6(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere is a valid joint probability density function. (a) Find E(Y1|Y2 = y2). E(Y1|Y2 = y2) = (b) Use the answer derived in part (a) to find E(Y1). (Compare this with E(Y1) found using the marginal density function f1(y1) = 3(1 − y1)2.) E(Y1) =

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answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

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