Question

In: Statistics and Probability

Suppose X and Y are independent variables and X~ Bernoulli(1/2) and Y~ Bernoulli(1/3) and Z=X+Y A-...

Suppose X and Y are independent variables and X~ Bernoulli(1/2) and Y~ Bernoulli(1/3) and Z=X+Y

A- find the joint probability table

B- find the probility distribution table of Z

C- find E(X+Y)

D- find E(XY)

E- find Cov(X, Y)

Solutions

Expert Solution


Related Solutions

Suppose X and Y are independent random variables with X = 2:8 and Y = 3:7....
Suppose X and Y are independent random variables with X = 2:8 and Y = 3:7. Find X+Y , the standard deviation of X + Y .
Suppose X and Y are independent random variables and take values 1, 2, 3, and 4...
Suppose X and Y are independent random variables and take values 1, 2, 3, and 4 with probabilities 0.1, 0.2, 0.3, and 0.4. Compute (a) the probability mass function of X + Y (b) E[X + Y ]?
Suppose that z = xy, where x and y are independent and normally distributed random variables
Suppose that z = xy, where x and y are independent and normally distributed random variables. The mean and variance of x are µx = 10 and σ2x = 2. The mean and variance of y are µy = 15 and σ2y = 3. Find the mean and variance of z by simulation. Does µz = µxµy? Does σ2z = σ2x σ2y? Do this for 100, 1000, and 5000 trials.
Suppose X, Y, and Z are independent Gaussian random variables with σx = 0.2, σy =...
Suppose X, Y, and Z are independent Gaussian random variables with σx = 0.2, σy = 0.3, σz = 1, μx=3.0, μy=7.7, and μz = 0 Determine the following: (a) The joint PDF of X, Y, and Z (b) Pr( (7.6<Y<7.8) | (X<3, Z<0) c) The Correlation matrix and covariance matrix of X, Y, and Z
Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z...
Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z := X + Y ? (b) Find the pdf of Z. (c) Find MZ(t). (d) Let U = e Y . What is the range of U? (e) Find the pdf of U|X.
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...
Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution...
Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution formula
Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the...
Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the correlation coefficient between (X-2YX+1) and (4X+Y)
Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2,...
Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2, 4]). a) FindP(X<Y). b) FindP(X<Y|Y>3) c) FindP(√Y<X<Y).
1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2...
1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2 1B) Use the Divergence Theorem to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT