# Question: A colleague of your proposes that a certain pair of

A colleague of your proposes that a certain pair of random variables be modeled with a joint CDF of the form

Fx, y (x,y) = [1 – ae–x – be–y +ce–(x+y)] u (x) u (y).

(a) Find any restrictions on the constants a, b, and c needed for this to be a valid joint CDF.

(b) Find the marginal CDFs, and under the restrictions found in part (a).

Fx, y (x,y) = [1 – ae–x – be–y +ce–(x+y)] u (x) u (y).

(a) Find any restrictions on the constants a, b, and c needed for this to be a valid joint CDF.

(b) Find the marginal CDFs, and under the restrictions found in part (a).

**View Solution:**## Answer to relevant Questions

Suppose a pair of random variables is uniformly distributed over a rectangular region, A: x1 < X < x2, y1 < Y < y2. Find the conditional PDF (X, Y) of given the conditioning event (X, Y) Ɛ B, where the region B is an ...Two random variables X and Y have, μx = 2, μy = –1, σx = 1, σy = 4, and p X,Y = 1 / 4. Let U = X + 2Y and V = 2X –Y. Find the following quantities: (a)E [U] and E [V]; (b)E [U] , and E [V2]; (c)E [UV], Cov (U, V), ...Find an example (other than the one given in Example 5.15) of two random variables that are uncorrelated but not independent. Two random variables have a joint Gaussian PDF given by Find E [X], E [Y], Var (X), VAr (Y), ρ X,Y, Cov (X,Y), and E[XY]. (a) Given the joint characteristic function of a pair of random variables, Φ X, Y (ω1, ω2). How do we get a marginal characteristic function of one of the random variables, say, Φ X (ω) from the joint characteristic ...Post your question