Question 6 . Let X and Y be independent random variables each having density function Determine...

Question 6 .

Let X and Y be independent random variables each having density function

Determine E(Y ), E(X), E(Y ² + X), E(X.Y ).
Determine Variance σ_X² and the standard deviation σ_Y .
If a new random variable Z is such that Z = 3X + 2Y + 2, determine E(Z).

Answers :

Solutions

Expert Solution

ANSWER::

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

orchestra answered 2 years ago

Next > < Previous

Related Solutions

. 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 ..

If X and Y are independent exponential random variables, each having parameter λ = 6, find...

If X and Y are independent exponential random variables, each having parameter λ = 6, find the joint density function of U = X + Y and V = e 2X. The required joint density function is of the form fU,V (u, v) = { g(u, v) u > h(v), v > a 0 otherwise (a) Enter the function g(u, v) into the answer box below. (b) Enter the function h(v) into the answer box below. (c) Enter the value...

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)=...

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

Let X and Y be independent continuous random variables, with each one uniformly distributed in the...

Let X and Y be independent continuous random variables, with each one uniformly distributed in the interval from 0 to1. Compute the probability of the following event. XY<=1/7

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y is a uniform (0,6). Let W=2X-Y and Z= 2X+Y. a) Find the expected value of X, the expected value of Y, the variance of X and the variance of Y. b) Find the expected value of W. c) Find the variance of W. d) Find the covariance of Z and W. d) Find the covariance of Z and W.

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...

Let X, Y and Z be independent random variables, each uniformly distributed on the interval (0,1)....

Let X, Y and Z be independent random variables, each uniformly distributed on the interval (0,1). (a) Find the cumulative distribution function of X/Y. (b) Find the cumulative distribution function of XY. (c) Find the mean and variance of XY/Z.

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y...

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y ) is uniformly distributed on [0, 1]. (Please solve it with clear explanations so that I can learn it. I will give thumbs up.)

Assume that X, Y, and Z are independent random variables and that each of the random...

Assume that X, Y, and Z are independent random variables and that each of the random variables have a mean of 1. Further, assume σX = 1, σY = 2, and σZ = 3. Find the mean and standard deviation of the following random variables: a. U = X + Y + Z b. R = (X + Y + Z)/3 c. T = 2·X + 5·Y d. What is the correlation between X and Y? e. What is the...

Subjects