Question

Let X and Y be independent random variables each having the uniform distribution on [0, 1]....

Let X and Y be independent random variables each having the uniform distribution on [0, 1].

(1)Find the conditional densities of X and Y given that X > Y .

(2)Find E(X|X>Y) and E(Y|X>Y) .

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
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? =...
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? = ?, ? = ?) = 1 − ?, ?(? = 1|? = ?, ? = ?) = ?(1 − ?) and ?(? = 2|? = ?, ? = ?) = ??. 1. Find the conditional joint p.d.f. (the posterior) ??,?|?=?. 2.Write down the conditional expectation ?[?|? = ?] and ?[?|? = ?] as functions of ?.
X and Y are independent variables, with X having a uniform (0,1) distribution and Y being...
X and Y are independent variables, with X having a uniform (0,1) distribution and Y being an exponential random variable with a mean of 1. Given this information, find P(max{X,Y} > 1/2)
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? =...
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? = ?, ? = ?) = 1 − ?, ?(? = 1|? = ?, ? = ?) = ?(1 − ?) and ?(? = 2|? = ?, ? = ?) = ??. 1.Write down the conditional expectation ?[?|? = ?] and ?[?|? = ?] as functions of ?.
Let X and Y be independent random variables, with X following uniform distribution in the interval...
Let X and Y be independent random variables, with X following uniform distribution in the interval (0, 1) and Y has an Exp (1) distribution. a) Determine the joint distribution of Z = X + Y and Y. b) Determine the marginal distribution of Z. c) Can we say that Z and Y are independent? Good
Let U1 and U2 be independent Uniform(0, 1) random variables and let Y = U1U2. (a)...
Let U1 and U2 be independent Uniform(0, 1) random variables and let Y = U1U2. (a) Write down the joint pdf of U1 and U2. (b) Find the cdf of Y by obtaining an expression for FY (y) = P(Y ≤ y) = P(U1U2 ≤ y) for all y. (c) Find the pdf of Y by taking the derivative of FY (y) with respect to y (d) Let X = U2 and find the joint pdf of the rv pair...
Let X, Y, and Z be independent and identically distributed discrete random variables, with each having...
Let X, Y, and Z be independent and identically distributed discrete random variables, with each having a probability distribution that puts a mass of 1/4 on the number 0, a mass of 1/4 at 1, and a mass of 1/2 at 2. a. Compute the moment generating function for S= X+Y+Z b. Use the MGF from part a to compute the second moment of S, E(S^2) c. Compute the second moment of S in a completely different way, by expanding...
(a) Given two independent uniform random variables X, Y in the interval (−1, 1), find E...
(a) Given two independent uniform random variables X, Y in the interval (−1, 1), find E |X − Y |. (b) Let X, Y be as in (a). Find the support and density of the random variable Z = |X − Y |. (c) From (b), compute the mean of Z and check whether you get the same answer as in (a)
The joint probability density function of two random variables X and Y is f(x, y) =...
The joint probability density function of two random variables X and Y is f(x, y) = 4xy for 0 < x < 1, 0 < y < 1, and f(x, y) = 0 elsewhere. (i) Find the marginal densities of X and Y . (ii) Find the conditional density of X given Y = y. (iii) Are X and Y independent random variables? (iv) Find E[X], V (X) and covariance between X and Y .
Let X and Y be independent random variables, uniformly distribued on the interval [0, 2]. Find...
Let X and Y be independent random variables, uniformly distribued on the interval [0, 2]. Find E[e^(X+Y) ].
Let continuous random variables X, Y be jointly continuous, with the following joint distribution fXY​(x,y) =...
Let continuous random variables X, Y be jointly continuous, with the following joint distribution fXY​(x,y) = e-x-y ​for x≥0, y≥0 and fXY(x,y) = 0 otherwise​. 1) Sketch the area where fXY​(x,y) is non-zero on x-y plane. 2) Compute the conditional PDF of Y given X=x for each nonnegative x. 3) Use the results above to compute E(Y∣X=x) for each nonnegative x. 4) Use total expectation formula E(E(Y∣X))=E(Y) to find expected value of Y.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT