Consider continuous bivariate random variables X and Y with

Consider continuous bivariate random variables, X and Y, with the following joint PDF (c is a constant): Find the value of c for which this is a valid PDF Compute P(X 1.25, Y 0.75) Find f_X(x), the marginal distribution of X Compute P(1.3

Solution

a)c=1

b)0.015625

c)f_x(x)=x-(1/2)

d)1.885

e)19/12 =1.583333

f)11/144

g) f_y|X=x(y)=2(x-y)/(2x-1)

h) 3.5/3 =1.166667

i) 0.15625