Question

Assume that two random variables X and Y satisfy E(X|Y ) = Y and E(Y |X)...

Assume that two random variables X and Y satisfy E(X|Y ) = Y and E(Y |X) = X. Show that P(X = Y ) = 1.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Assume two random variables X and Y satisfy the following joint PDF, fXY (x, y) =...
Assume two random variables X and Y satisfy the following joint PDF, fXY (x, y) = { 2, x + y ≤ 1 x, y ≥ 0, 0, otherwise.} (a) Find the values of E[X + Y ] and E[X − Y ]. (b) Derive g(s) = E[X − Y |X + Y = s] for any given s. (c) Derive h(t) = E[X + Y |X − Y = t] for any given t.
Let two random variables X and Y satisfy Y |X = x ∼ Poisson (λx) for...
Let two random variables X and Y satisfy Y |X = x ∼ Poisson (λx) for all possible values x from X, with λ being an unknown parameter. If (x1, Y1), ...,(xn, Yn) is a random sample from the random variable Y |X = x, construct the estimator for λ using the method of maximum likelihood and determine its unbiasedness.
(a) When are two random variables X and Y independent? (b) Show that if E(XY )...
(a) When are two random variables X and Y independent? (b) Show that if E(XY ) = E(X)E(Y ) then V ar(X + Y ) = V ar(X) + V ar(Y ).
Consider two random variables X and Y such that E(X)=E(Y)=120, Var(X)=14, Var(Y)=11, Cov(X,Y)=0. Compute an upper...
Consider two random variables X and Y such that E(X)=E(Y)=120, Var(X)=14, Var(Y)=11, Cov(X,Y)=0. Compute an upper bound to P(|X−Y|>16)
Consider the following bivariate distribution p(x, y) of two discrete random variables X and Y. Y\X...
Consider the following bivariate distribution p(x, y) of two discrete random variables X and Y. Y\X -2 -1 0 1 2 0 0.01 0.02 0.03 0.10 0.10 1 0.05 0.10 0.05 0.07 0.20 2 0.10 0.05 0.03 0.05 0.04 a) Compute the marginal distributions p(x) and p(y) b) The conditional distributions P(X = x | Y = 1) c) Are these random variables independent? d) Find E[XY] e) Find Cov(X, Y) and Corr(X, Y)
Suppose X,Y are discrete random variables, each taking only two distinct values. Prove that if E(XY)=E(X)E(Y)...
Suppose X,Y are discrete random variables, each taking only two distinct values. Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be aware that you have to prove E(XY) =E(X)E(Y) -> X,Y independent and NOT the converse)
Consider two random variables, X and Y, with joint PDF fxy(x,y)=e-2|y-x^2|-x    x>=0 , y can...
Consider two random variables, X and Y, with joint PDF fxy(x,y)=e-2|y-x^2|-x    x>=0 , y can be any value fxy(x,y)=0 otherwise (1) Determine fY|X(y|x) (2)Determine E[Y|X=x]
Consider two random variables X and Y . X can take the values 0, 1 and...
Consider two random variables X and Y . X can take the values 0, 1 and 2 andY cantakethevalues0and1. Youaretoldthat: P(X=0)=0.4,P(X=1)=0.2, P(Y =0|X=0)=0.4,P(Y =0|X=1)=0.2,P(Y =0|X=2)=0.3. Calculate P(Y =1),E(Y),Cov(X,Y),P(X=0|Y =0),P(Y =1|X+Y ≤2)
Problems 1. Two independent random variables X and Y have the probability distributions as follows: X...
Problems 1. Two independent random variables X and Y have the probability distributions as follows: X 1 2 5 P (X) 0.2 0.5 0.3 Y 2 4 P (Y) 0.7 0.3 a) Let T = X + Y. Find all possible values of T. Compute μ and . T σ T b) Let U = X - Y. Find all possible values of U. Compute μ U and σ U . c) Show that μ T = μ X +...
. Let X and Y be two discrete random variables. The range of X is {0,...
. Let X and Y be two discrete random variables. The range of X is {0, 1, 2}, while the range of Y is {1, 2, 3}. Their joint probability mass function P(X,Y) is given in the table below: X\Y        1             2              3 0              0              .25          0 1              .25          0             .25 2              0             .25          0 Compute E[X], V[X], E[Y], V[Y], and Cov(X, Y).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT