Question

3. Suppose the joint PDF of two random variables X and Y are given below 3(xy2 + x2y), if o sxs 1,0 Sy s 1, fx.x (x,y) otherwise. (1) What is the covariance of X and Y? (20 points) (2) What is the correlation between X and Y? (20 points) 0,

Answer 1

Vor (x)E(X2)- E(X) - 33 - 02 281 576 0.50 = 0.55 - = 0.05 Var(x) = Var (Y) Cov(x,y) ſ vary Very Form No. 6 - to 10.05 50.05 - 0.00173 10.22360)(0.22360) -0.00173 0.04999 = -0.034600

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Page No. : Covariance of X and Y : cov (x,y) = E(XY)- E(X) ELY) - 5-14X55) - 289 576 288 - 289 576 cov (x,y) - - (2) 576 Correlation between x and y Correlation 1P) Cox (x, y) Var X Vary Var X = E(x?) – E (x)? Van Y= k172) - ELYSE E(X)= Shafenly) dy dx = Shu 3 (ny?r ug) dy de

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