Find the conditional p.d.f.’s f(y|x) and f(z|x, y).
Find the conditional p.d.f.’s f(y|x) and f(z|x, y). 4. Suppose that random variables (X, Y, Z)...
Let X and Y be random variables for which the joint p.d.f. is as follows: f (x, y) = 2(x + y) for 0 ≤ x ≤ y ≤ 1, 0 otherwise.Find the cumulative distribution function (c.d.f.) of X and Y.Find p.d.f. of Z=X+Y.
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
3. (16 points) Suppose that X and Y have the following joint p.d.f. f(x,y) = for 0 < x < y,0 < y <, y 0 otherwise. Compute E[X2]y], the expectation of the conditional distribution of x2 given Y = y.
qkx Q.3 (20 pts) The joint p.d.f. of 2 random variables x and y is given by f xy(x,y) = 05x,0 sy.(2x + y) = 2 to otherwise Where k is a constant. 1) (5 pts) Find the value of k. 2) (5 pts) Are x and y independent? Explain. 3) (10 pts) Define z = 2x-y. Find the p.d.f. of z.
Two random variables, X and Y, have joint probability density function f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1 0 , o t h e r w i s e Find c value. What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y. Find the conditional expectation E [...
Suppose that X and Y are continuous random variables with the following joint p.d.f.: (a) Find fX|Y =y(x|y). (b) Calculate EX[X|Y = y] (c) Calculate VarX[X|Y = y] (d) Calculate E[Y] (e) Show that VarY [EX(X|Y = y)] = VarY [2/3Y ]. (f) Find VarX(X|Y = 1/2) (g) Find EX[X|Y = 0.2] (h) Without any calculation, what is P(X < Y )? Explain your answer. (i) Without any calculation, what is FX,Y (2,2)? Explain your answer. fxy(x, y)- o otherwise
Find Var(2X-Y) Two random variables X and Y are i.i.d. and their common p.d.f. is given by f )- c(1+r) if 0 <r < 1. otherwise. f(3) = 10
Suppose X, Y and Z are random variables with joint pdf f(x,y,z) = cxy2z if 0 < x ≤ 2, 0 ≤ y < 1, 0 < z < 1 0 otherwise a.) Find the constant c b.) Calculate P(1 < X ≤ 2, 0.5 ≤ Y < 1) c.) Calculate E(2X+2020) d.) Calculate Var(2X+2020) e.) Calculate E(XZ+2020) I think I understand how to do parts a and c, but I'm less certain of how to proceed on the rest...
1) Suppose that three random variables, X, Y, and Z have a continuous joint probability density function f(x, y. z) elsewhere a) Determine the value of the constant b) Find the marginal joint p. d. fof X and Y, namely f(x, y) (3 Points) c) Using part b), compute the conditional probability of Z given X and Y. That is, find f (Z I x y) d) Using the result from part c), compute P(Z<0.5 x - 3 Points) 2...