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1. Let X be the amount of water in a two gallon container in the fridge...

1. Let X be the amount of water in a two gallon container in the fridge of the Jones household at the start of the day and let Y denote the amount dispensed rom that two gallon container during that day. We assume that (X,Y) has joint density. f(x,y) = (xy)/2, 0<y<x<2.

a. Find the marginal density of X.

b. Find E(XY)

c. find the conditional density off Y given X=x

d. Are X and Y independent?

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Answer #1

fron, y) = xyl i ocy23<? ☺ fx 10 = !. f(ydy = aydy - english - *(?) = OLE ( E(Xys Slear. franys dedy = I layan dads 2 [aido

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