Let R be a random variable with an exponential distribution with parameter α = 1. Conditional...

Question

Question

Let R be a random variable with an exponential distribution with parameter α = 1. Conditional on R, Y has pdf

f_y|R (y|r) = { ry 0<=y<= sqrt(r/2); otherwise 0

Determine the conditional pdf of R given Y .

math Statistics-And-Probability

Answer 1

Answer #1

thank you

Answer 2

Similar Homework Help Questions

Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is expo...

Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
3. Let X be an exponential random variable with parameter 1 = $ > 0, (s...

3. Let X be an exponential random variable with parameter 1 = $ > 0, (s is a constant) and let y be an exponential random variable with parameter 1 = X. (a) Give the conditional probability density function of Y given X = x. (b) Determine ElYX]. (c) Find the probability density function of Y.
Let X be an exponential random variable with parameter A > 0, and let Y be...

Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of a toss of a fair coin Compute the CDF and the PDF of Z = XY Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of...

Problem 3 [5 points) (a) [2 points] Let X be an exponential random variable with parameter...

Problem 3 [5 points) (a) [2 points] Let X be an exponential random variable with parameter 1 =1. find the conditional probability P{X>3|X>1). (b) [3 points] Given unit Gaussian CDF (x). For Gaussian random variable Y - N(u,02), write down its Probability Density Function (PDF) [1 point], and express P{Y>u+30} in terms of (x) [2 points)
Let X be an exponential random variable with parameter 1 = 2, and let Y be...

Let X be an exponential random variable with parameter 1 = 2, and let Y be the random variable defined by Y = 8ex. Compute the distribution function, probability density function, expectation, and variance of Y
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with ...

Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...

Let X and Y be a random variable with joint PDF: fxx (x, y) = {...

Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
The PDF of random variable X and the conditionalPDF of random variable Y given X are...

The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...
Let X and Y be a random variable with joint PDF: f X Y ( x...

Let X and Y be a random variable with joint PDF: f X Y ( x , y ) = { a y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise What is a? What is the conditional PDF of given ? What is the conditional expectation of given ? What is the expected value of ? Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...

2. Let R be a continuous random variable with the following conditional distribution Rlo~N(0, o2) where...

2. Let R be a continuous random variable with the following conditional distribution Rlo~N(0, o2) where o is a discrete valued random variable with the following distribution 1 P(o 1) P(o 100) =. 2 Compute the mean, variance and kurtosis of the random variable R. Hint: use the double expectation formula 2. Let R be a continuous random variable with the following conditional distribution Rlo~N(0, o2) where o is a discrete valued random variable with the following distribution 1 P(o...