Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X − Y) = 2, what is cov(X,Y)? also Prove that if X and Y are independent random variables, then Var(XY) = Var(X)Var(Y) +E[X] 2 Var(Y) +E[Y] 2 Var(X). Please please help ill br thankful please

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

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Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)2)? %3D

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Q: Suppose that X and Y are random variables. If we know that V(X)=11 and Y=2X−4, determine σ(Y).

A: Given : V(X)=11 and Y=2X−4 V(Y) = V(2X−4) = 22V(X) = 4*11 = 44

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Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

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Q: Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use…

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Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find…

A: Solution (2) There is two different questions So i am solving first

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Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

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Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 < Y < 16) = P(A < X < B) μX=5σX=3μY=-2σY=6

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Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

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Q: Let X and Y be two random variables such that Cov(X.Y)=-3. Then cov(3X+5,-2Y+5)=18…

A: It is given that The covariance between X and Y is Cov(X, Y) = -3 We know that Cov(aX+b, cY+d) =…

Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0≤x≤ 1. Find…

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Q: Suppose X1, X2, X3 and X4 are independent random variables, which have the same Bernoulli…

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Q: Let X be a geometric random variable with parameter px parameter py 1/2 and let Y be a geometric…

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Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

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Q: Verify central limit theorem for the independent random variablesX,, where for each k, P{X =± 1} = .

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Q: Suppose that X, and X2 are random samples from a binomial distribution of two trials with parameter…

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Q: 5. Show that given random variables X and Y, Cov(X, E(Y | X)) = Cov(X, Y).

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Q: (6) Let X and Y be random variables with var(X) = 4, var(Y) = 9 and %3D var(X – Y) = 16. Then…

A: Given: Var(X) = 4 Var(Y) = 9 Var(X-Y) = 16

Q: If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 (5/2

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: An alternative proof of Theorem 2 may be based on the fact that if X1, X2, ..., and Xn are…

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Q: Let X1, X2, ..., Xn be independent and identically distributed random variables, X ∼ Exp(λ). Show…

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Q: To Construct:Random Variable X such that its first 2n moments

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Q: Let X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O…

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Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

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Q: Suppose that Alejandro is planting a garden of tulips. Let X be the Bernoulli random variable that…

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