Question

. Let X and Y be two discrete random variables. The range of X is {0,...

. Let X and Y be two discrete random variables. The range of X is {0, 1, 2}, while the range of Y is {1, 2, 3}. Their joint probability mass function P(X,Y) is given in the table below:

X\Y        1             2              3

0              0              .25          0

1              .25          0             .25

2              0             .25          0

Compute E[X], V[X], E[Y], V[Y], and Cov(X, Y).

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
Let X, Y be two random variables with a joint pmf f(x,y)=(x+y)/12 x=1,2 and y=1,2 zero...
Let X, Y be two random variables with a joint pmf f(x,y)=(x+y)/12 x=1,2 and y=1,2 zero elsewhere a)Are X and Y discrete or continuous random variables? b)Construct and joint probability distribution table by writing these probabilities in a rectangular array, recording each marginal pmf in the "margins" c)Determine if X and Y are Independent variables d)Find P(X>Y) e)Compute E(X), E(Y), E(X^2) and E(XY) f)Compute var(X) g) Compute cov(X,Y)
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)
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...
Let X and Y be discrete random variables, their joint pmf is given as Px,y =...
Let X and Y be discrete random variables, their joint pmf is given as Px,y = ?(? + ? + 2)/(B + 2) for 0 ≤ X < 3, 0 ≤ Y < 3 Where B=2. a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 2
Let X and Y be a random variables with the joint probability density function fX,Y (x,...
Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { e −x−y , 0 < x, y < ∞ 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 .
X/Y 1 2 3 4 -1 0 0 0.1 0.2 0 0.1 0.1 0 0.1 1...
X/Y 1 2 3 4 -1 0 0 0.1 0.2 0 0.1 0.1 0 0.1 1 0.2 0 0.1 0.1 let the joint probability mass function of the discrete random variable X and Y give as above Find E(3x+1) and E(3x+4y) cov( X,Y)
Let X and Y be discrete random variables, their joint pmf is given as ?(x,y)= ?(?...
Let X and Y be discrete random variables, their joint pmf is given as ?(x,y)= ?(? + ? − 2)/(B + 1) for 1 < X ≤ 4, 1 < Y ≤ 4 Where B is the last digit of your registration number ( B=3) a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 3
SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...
SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf is given as Px,y = ?(? + ?)/(B + 1) for 0 < X ≤ 3, 0 < Y ≤ 3 (Where B=5) a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 2
Let X and Y be continuous random variables with joint distribution function F(x, y), and let...
Let X and Y be continuous random variables with joint distribution function F(x, y), and let g(X, Y ) and h(X, Y ) be functions of X and Y . Prove the following: (a) E[cg(X, Y )] = cE[g(X, Y )]. (b) E[g(X, Y ) + h(X, Y )] = E[g(X, Y )] + E[h(X, Y )]. (c) V ar(a + X) = V ar(X). (d) V ar(aX) = a 2V ar(X). (e) V ar(aX + bY ) = a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT