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please show all the steps and in order Q.5 Let X and Y be continuous rvs...

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Statistics

please show all the steps and in order

Q.5 Let X and Y be continuous rvs with the joint pdf

f(x, y) = 60(x^2)y, for 0 < x, 0 < y, 0 < x + y< 1 and 0 otherwise.

(a) Find E[X + Y ] and E[X − Y ]

(b) Find E[XY ]

(c) Find E[Y |X = x] and E[X|Y = y].

(d) Find Cov[X, Y ]

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