Question

The probability distribution of a couple of random variables (X, Y) is given by : X/Y...

The probability distribution of a couple of random variables (X, Y) is given by :

X/Y 0 1 2
-1 a 2a a
0 0 a a
1 3a 0 a

1) Find "a"

2) Find the marginal distribution of X and Y

3) Are variables X and Y independent?

4) Calculate V(2X+3Y) and Cov(2X,5Y)

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

Homework Answers

Answer #1

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
The joint probability distribution of two random variables X and Y is given in the following...
The joint probability distribution of two random variables X and Y is given in the following table X Y → ↓ 0 1 2 3 f(x) 2 1/12 1/12 1/12 1/12 3 1/12 1/6 1/12 0 4 1/12 1/12 0 1/6 f(y) a) Find the marginal density of X and the marginal density of Y. (add them to the above table) b) Are X and Y independent? c) Compute the P{Y>1| X>2} d) Compute the expected value of X. e)...
Consider joint Probability distribution of two random variables X and Y given as following f(x,y)   X...
Consider joint Probability distribution of two random variables X and Y given as following f(x,y)   X        2   4   6 Y   1   0.1   0.15   0.06    3   0.17   0.1   0.18    5   0.04   0.07   0.13 (a)   Find expected value of g(X,Y) = XY2 (b)   Find Covariance of Cov(x,y)
a) The joint probability density function of the random variables X, Y is given as f(x,y)...
a) The joint probability density function of the random variables X, Y is given as f(x,y) = 8xy    if  0≤y≤x≤1 , and 0 elsewhere. Find the marginal probability density functions. b) Find the expected values EX and EY for the density function above c) find Cov  X,Y .
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
Problem 4 The joint probability density function of the random variables X, Y is given as...
Problem 4 The joint probability density function of the random variables X, Y is given as f(x,y)=8xy if 0 ≤ y ≤ x ≤ 1, and 0 elsewhere. Find the marginal probability density functions. Problem 5 Find the expected values E (X) and E (Y) for the density function given in Problem 4. Problem 7. Using information from problems 4 and 5, find Cov(X,Y).
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) =...
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1 = 0, otherwise a) Find marginal density of Y, fy(y) b) Calculate E[X | Y = 0]
Problems 9 and 10 refer to the discrete random variables X and Y whose joint distribution...
Problems 9 and 10 refer to the discrete random variables X and Y whose joint distribution is given in the following table. Y=-1 Y=0 Y=1 X=1 1/4 1/8 0    X=2 1/16 1/16 1/8 X=3 1/16 1/16 1/4 P9: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and Var(Y). P10: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent?
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)
The independent random variables X and Y are defined by the following probability distribution tables: X...
The independent random variables X and Y are defined by the following probability distribution tables: X 1 3 6 f(x) 0.6 0.3 0.1 Y 2 3 5 7 f(y) 0.1 0.2 0.3 0.4Determine the standard deviation of 3Y + 5
Let random variables X and Y follow a bivariate Gaussian distribution, where X and Y are...
Let random variables X and Y follow a bivariate Gaussian distribution, where X and Y are independent and Cov(X,Y) = 0. Show that Y|X ~ Normal(E[Y|X], V[Y|X]). What are E[Y|X] and V[Y|X]?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT