Let X and Y be independent geometric random variables with parameter p. Find the pmf of...

Let X and Y be independent geometric random variables with parameter p. Find the pmf of X + Y

Expert Solution

orchestra answered 2 years ago

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 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∼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 ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2...

Let X ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2 fX(2) = 1 2 fY (3) = 1 3 fY (4) = 2 3 Answer the following questions (a) Write down the joint PMF (b) Calculate P(X + Y 6 5) and P(Y −X > 2) (c) Calculate E(XY ), E(X2Y ), E(︁X2+1 Y−2)︁ (d) Calculate the Cov(X,Y ), Cov(1−X,3Y + 2) and Var(2X −Y ) ( e*) Calculate Cov(XY,X), Cov(XY,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

If X and Y are independent exponential random variables, each having parameter λ = 6, find...

If X and Y are independent exponential random variables, each having parameter λ = 6, find the joint density function of U = X + Y and V = e 2X. The required joint density function is of the form fU,V (u, v) = { g(u, v) u > h(v), v > a 0 otherwise (a) Enter the function g(u, v) into the answer box below. (b) Enter the function h(v) into the answer box below. (c) Enter the value...

let p ( x , y )be a joint pmf of Xand Y. p ( x...

let p ( x , y )be a joint pmf of Xand Y. p ( x , y ) y = 0 y = 1 y = 2 x = 0 .12 .10 .08 x = 1 .13 .17 .10 x = 2 .15 .15 0 (a) Find the marginal pmf's of Xand Y. (b) Determine whether Xand Yare independent. c) Find Correlation (X,Y)

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

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 two independent random variables. X is a binomial (25,0.4) and Y...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y is a uniform (0,6). Let W=2X-Y and Z= 2X+Y. a) Find the expected value of X, the expected value of Y, the variance of X and the variance of Y. b) Find the expected value of W. c) Find the variance of W. d) Find the covariance of Z and W. d) Find the covariance of Z and W.

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