Question

Let X and Y be random variables with the following distributions X N~ (20,2) and Y...

Let X and Y be random variables with the following distributions X N~ (20,2) and Y N~ (30,1). The covariance of X and Y is σ XY = 0.25 . Let Z= + 0.75X x 0.25Y . Find the mean and the variance of Z.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The solution of the above question is given below:

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
STAT 180 Let X and Y be independent exponential random variables with mean equals to 4....
STAT 180 Let X and Y be independent exponential random variables with mean equals to 4. 1) What is the covariance between XY and X. 2) Let Z = max ( X, Y). Find the Probability Density Function (PDF) of Z. 3) Use the answer in part 2 to compute the E(Z).
Let X and Y be independent random variables following Poisson distributions, each with parameter λ =...
Let X and Y be independent random variables following Poisson distributions, each with parameter λ = 1. Show that the distribution of Z = X + Y is Poisson with parameter λ = 2. using convolution formula
Let X and Y be random variables, P(X = −1) = P(X = 0) = P(X...
Let X and Y be random variables, P(X = −1) = P(X = 0) = P(X = 1) = 1/3 and Y take the value 1 if X = 0 and 0 otherwise. Find the covariance and check if random variables are independent. How to check if they are independent since it does not mean that if the covariance is zero then the variables must be independent.
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y....
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y. What will be the distribution of Z? Hint: Use moment generating function.
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 +...
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as...
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as follows: Select X = x as a uniform random variable on [0,1]. Then, select Y as a Gaussian random variable with mean x and variance 1. Compute E[Y ]. b) Let X,Y be jointly Gaussian, with mean E[X] = E[Y ] = 0, variances V ar[X] = 1,V ar[Y ] = 1 and covariance Cov[X,Y ] = 0.4. Compute E[(X + 2Y )2].
Let X ~ N(1,3) and Y~ N(5,7) be two independent random variables. Find... Var(X + Y...
Let X ~ N(1,3) and Y~ N(5,7) be two independent random variables. Find... Var(X + Y + 32) Var(X -Y) Var(2X - 4Y)
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)
Let X and Y be independent and identically distributed random variables with mean μ and variance...
Let X and Y be independent and identically distributed random variables with mean μ and variance σ2. Find the following: a) E[(X + 2)2] b) Var(3X + 4) c) E[(X - Y)2] d) Cov{(X + Y), (X - Y)}
let X, Y be random variables. Also let X|Y = y ~ Poisson(y) and Y ~...
let X, Y be random variables. Also let X|Y = y ~ Poisson(y) and Y ~ gamma(a,b) is the prior distribution for Y. a and b are also known. 1. Find the posterior distribution of Y|X=x where X=(X1, X2, ... , Xn) and x is an observed sample of size n from the distribution of X. 2. Suppose the number of people who visit a nursing home on a day is Poisson random variable and the parameter of the Poisson...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT