6. Let the continuous-type random variables X and Y have the joint pdf f(x, y) = e' 0 < x < y < 0,0 elsewhere. (a) Compute the moment generating function (mgf) of (X, Y). (b) Use 6(a) to obtain the mgf of Z= Y - X and then give the density function for 7

Q: Show E(X)

A: Here given joint distribution of x and y

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A:

Q: Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table.…

A: The joint probability distribution of X and Y is f(x,y)   1       2       31           1/4    1/4…

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A: Given,  joint density function of x and y f(x,y) = e-x,0 if Z=X+2Y and W=X

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Q: 1) Let Y be a r.v which has the pdf as below f(y) (2)e-v²/0,y>0 = 0,0.w Using jacobian method find…

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A: *answer:

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A: Given that Total beans=458+162=620 Green beans=458 Yellow beans=162

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Q: fw=X+y, Find the probability density fu of the random vairiable W. g) W= 9, Find. the, probability…

A: where, ∫-∞∞∫-∞∞ f ( x,y ) dx dy = 1 x range is from y to 1,44 and y range is from 0 to x therefore,…

Q: 2. If X and Y are continuous random variables having joint density function if 0 < y < 1 and 0 < x <…

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Q: Let Y1,...,Yn denote a random sample from the density function given by fr (vla, 0) 1 ya-le- for y>…

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. b) Find the moment-generating…

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Q: (7) Find the marginal density of X when the conditional density of X given {Y = y} is Poisson(y) and…

A: 7. Note that X|Y=y is a discrete distribution and Y is continuous distribution. Given, X|Y=y ~…

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: Suppose that X and Y are statistically independent and identically distributed uniform random…

A: Let X and Y are independent random variable distributed uniform distrinution (0,1)The pdf functions…

Q: Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.

A:

Q: Let X and Y be two continuous random variables such that the joint density function i given by: f {…

A: Answer is 13/32.

Q: Find the density of X = max(Y1,Y2), where Y1 and Y2 are independent random variables with densities…

A: It is an important part of statistics . It is widely used .

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A:

Q: Suppose· X · has probability-density-function (p.d.f) fx(x) = 7(1+x²)³ ° which one is the p.d.f..…

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Q: (b) The expression for the joint probability density function of the transformed random variables U…

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A: a) The total probability is always 1. Using that we get:…

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Q: 1. The continuous uniform random variable X has density function 1 f(x) = a < x < B B – a' a) Find…

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Q: Let x(t) be a wide sense stationary random process with auto correction function R„(t) = e*1*1,…

A: Answer: For the given data,

Q: Suppose X is a gamma random variable gamma(a, B), where a > 1 and B > 0: x > 0 s(2) = { * a-le-/8…

A:

Q: A WSS process X (t) hus an auto correlation function Rxx (7) = e3la, Find its power spectral…

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Q: One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3|…

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Q: (3) Find the density of Y = X² when X ~ Binomial(4, ). The following answers are proposed: (a) P(Y =…

A:

Q: Show E(Y)

A: First we have to determine the marginal pdf of Y to calculate the value of E(Y).