Question: Consider two continuous random variables X and Y with joint p.d.f. f X, Y( x, y ) = x ^3 y C , 0 <

Consider two continuous random variables X and Y with joint p.d.f. f X, Y( x, y ) = x ^3 y C , 0< x<1, 0< y< 3 x, zero otherwise.

a) Find the value of C so that f X, Y( x, y ) is a valid joint p.d.f.

b) Find the marginal probability density function of X, f X( x ). Be sure to include its support.

c) Find the marginal probability density function of Y, f Y( y ). Be sure to include its support.

d) Find P( X Y ).

e) Find P( X + Y 1 ).

f) Find P( X Y 1 ).

g) Are X and Y independent? If not, find Cov ( X, Y ).

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