Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1,...

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1, P(X = 1, Y = 0) = .3, P(X = 2, Y = 0) = .2 P(X = 0, Y = 1) = .2, P(X = 1, Y = 1) = .2, P(X = 2, Y = 1) = 0.

a. Determine E(X) and E(Y ).

b. Find Cov(X, Y )

c. Find Cov(2X + 3Y, Y ).

Expert Solution

orchestra answered 1 year ago

Let X and Y be uniform random variables on [0, 1]. If X and Y are...

Let X and Y be uniform random variables on [0, 1]. If X and Y are independent, find the probability distribution function of X + Y

Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0<p<1....

Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0<p<1. (a) Find P(X>Y). (b) Find P(X+Y=n) and P(X=k|X+Y=n), for n=2,3,..., and k=1,2,...,n−1. I need an answer asap please. Thank you.

Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0...

Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0 < p < 1. (a) (6pts) Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y = n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1

Let X and Y be independent discrete random variables with the following PDFs: x 0 1...

Let X and Y be independent discrete random variables with the following PDFs: x 0 1 2 f(x)=P[X=x] 0.5 0.3 0.2 y 0 1 2 g(y)= P[Y=y] 0.65 0.25 0.1 (a) Show work to find the PDF h(w) = P[W=w] = (f*g)(w) (the convolution) of W = X + Y (b) Show work to find E[X], E[Y] and E[W] (note that E[W] = E[X]+E[Y])

1. Let X and Y be independent U[0, 1] random variables, so that the point (X,...

1. Let X and Y be independent U[0, 1] random variables, so that the point (X, Y) is uniformly distributed in the unit square. Let T = X + Y. (a) Find P( 2Y < X ). (b). Find the CDF F(t) of T (for all real numbers t). HINT: For any number t, F(t) = P ( X <= t) is just the area of a part of the unit square. (c). Find the density f(t). REMARK: For a...

Let X and Y be independent and uniformly distributed random variables on [0, 1]. Find the...

Let X and Y be independent and uniformly distributed random variables on [0, 1]. Find the cumulative distribution and probability density function of Z = X + Y.

Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the...

Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the expected value E(XY ). b) What is the probability density function fZ(z) of Z = XY ? Hint: First compute the cumulative distribution function FZ(z) = P(Z ≤ z) using a double integral, and then differentiate in z. c) Use your answer to b) to compute E(Z). Compare it with your answer to a).

Let X and Y be independently and identically distributed random variables. Then, what is P (X...

Let X and Y be independently and identically distributed random variables. Then, what is P (X < Y ) (a) in case the common distribution of X and Y is continuous? (b) in case P(X=i)=P(Y =i)= 1, i=1,2,···,n.

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i) find the marginal pdf of X and Y respectively, ii) the conditional pdf of Y given x, that is fY|X(y|x), iii) E(Y|x) and Corr(X,Y).

9.8 Let X and Y be independent random variables with probability distributions given by P(X =...

9.8 Let X and Y be independent random variables with probability distributions given by P(X = 0) = P(X = 1) = 1/2 and P(Y = 0) = P(Y = 2) = 1/2 . a. Compute the distribution of Z = X + Y . b. Let Y˜ and Z˜ be independent random variables, where Y˜ has the same distribution as Y , and Z˜ the same distribution as Z. Compute the distribution of X˜ = Z˜ − Y

Question