A hint about expected length in rectangle with base 1 and height 2...X is uniformly drawn from [0'1] ...so expected value of X is 1/2 ..Y is uniformly drawn from [0'2] ...so expected value of Y is 1... So it is expected that randomly chosen point will be (1/2' 1) ..and the length of line joining (0' 0) to this point is square-root(1/4+1) = √5/2 ....so now u have to prove this systematically using PDF and integration...
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