Let X and Y be continuous random variables with joint p.d.f. f(x, y) = k(x + y), 0≤x≤y≤1 Find the (a) (b) value of the constant k joint c.d.f of X and Y F(x, y) marginal c.d.f. of X and marginal c.d.f. of Y. CX ginal ndf of Y

The joint probability distribution of the random variables is f(x,y)= 8xy, 0<=y<=x<=1. fine the covarience of x and y

Consider the pair of random variables ( X , Y ) with joint PDF f X , Y ( x , y ) = 2 for 0 ≤ x ≤ y ≤ 1 and f X , Y ( x , y ) = 0 otherwise. (In particular, note that the joint PDF is only nonzero when x ≤ y .) (a) Draw a picture of the range of ( X , Y ) in the x y -plane. (b) Describe the conditional distribution of X given Y = y , for 0 ≤ y ≤ 1 . (c) What is the marginal PDF f X of X ? (d) Are X and Y independent?

Let X ~ N(1,2) and Y ~ N(4, 7) be independent random variables. Find the probability P(X + Y > 0):