. Let X and Y be a random variables with the joint probability density function fX,Y...

. Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { 1, 0 < x, y < 1 0, otherwise } . a. Let W = max(X, Y ) Compute the probability density function of W. b. Let U = min(X, Y ) Compute the probability density function of U. c. Compute the probability density function of X + Y ..

Expert Solution

orchestra answered 2 years ago

The joint probability density function for two random variables X and Y is given as, fx,y...

The joint probability density function for two random variables X and Y is given as, fx,y (x, y) = (2/3)(1 + 2xy3 ), 0 < x < 1, 0 < y < 1 (a) Find the marginal probability density functions for X and Y . (b) Are X and Y independent? Justify your answer. (c) Show that E[X] = 4/9 and E[Y ] = 7/15 . (d) Calculate Cov(X, Y )

Let X and Y be two continuous random variables with the joint probability density function of...

Let X and Y be two continuous random variables with the joint probability density function of for 0 < x < 2, 0 < y < 2, x + y < 1,where c is a constant. (In all the following answers, you do NOT need to find what the value of c is; just treat it as a number.) (a) Write out the marginal distribution of Y. (b) P(Y < 1/3) = ? (c) P(X < 1.5, Y < 0.5)=...

If the joint probability density function of the random variables X and Y is given by...

If the joint probability density function of the random variables X and Y is given by f(x, y) = (1/4)(x + 2y) for 0 < x < 2, 0 < y < 1, 0 elsewhere (a) Find the conditional density of Y given X = x, and use it to evaluate P (X + Y/2 ≥ 1 | X = 1/2) (b) Find the conditional mean and the conditional variance of Y given X = 1/2 (c) Find the variance...

1. Let X be a random variable with probability density function fX given by fX(x) =...

1. Let X be a random variable with probability density function fX given by fX(x) = γαγ/ (x + α)^γ+1 , x ≥ 0, 0, x < 0, where α > 0 and γ > 0. (a) Find the cumulative distribution function (cdf) FX of X. (b) Let Y = log(X+α /α) . Find the cdf of Y and identify the distribution. (c) How could a realisation of X be generated from an R(0,1) random number generator? (d) Let Z...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) =...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) = { 1, 0 ≤ ? ≤ 2,0 ≤ ? ≤ 1,2? ≤ ? 0, otherwise 1) Find the correlation coefficient ??? between the two random variables X and Y Find the probability P(Y>X/2). help please asap

Let X be a continuous random variable with a probability density function fX (x) = 2xI...

Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e −x a. Find the expression for the probability density function fY (y). b. Find the domain of the probability density function fY (y).

Let (X, Y) be a random vector with a function of the joint density given by...

Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y) a) Determine k so that f X, Y (x, y) is a true probability density function joint quality. b) Determine the marginal probability density functions of X and Y. c) Calculate P (3 <X <4, Y> 2). d) Calculate P (X + Y> 4).

Let (X, Y) be a random vector with a function of the joint density given by...

Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y) a) Determine k so that f X, Y (x, y) is a true probability density function joint quality. b) Determine the marginal probability density functions of X and Y. c) Calculate P (3 <X <4, Y> 2). d) Calculate P (X + Y> 4).

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the following estimator of the intercept of the Best Linear Predictor: A = ?̅ - B • ?̅ , where ?̅ is the sample mean of y, ?̅ is the sample mean of x, and B is the sample covariance of Y and X divided by the sample variance of X. Identify the probability limit of A (if any). For each step in your derivation,...

Let X and Y be two discrete random variables whose joint probability distribution function is given...

Let X and Y be two discrete random variables whose joint probability distribution function is given by f(x, y) = 1 12 x 2 + y for x = −1, 1 and y = 0, 1, 2 a) Find cov(X, Y ). b) Determine whether X and Y are independent or not. (Justify your answer.

Question

. Let X and Y be a random variables with the joint probability density function fX,Y...

Solutions

Expert Solution

Related Solutions

The joint probability density function for two random variables X and Y is given as, fx,y...

Let X and Y be two continuous random variables with the joint probability density function of...

If the joint probability density function of the random variables X and Y is given by...

1. Let X be a random variable with probability density function fX given by fX(x) =...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) =...

Let X be a continuous random variable with a probability density function fX (x) = 2xI...

Let (X, Y) be a random vector with a function of the joint density given by...

Let (X, Y) be a random vector with a function of the joint density given by...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the...

Let X and Y be two discrete random variables whose joint probability distribution function is given...