Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y + 4Z) = 40, and Var(Z) = 2. a) If E(Y) = E(Z) = 1, what is E(Y2+Z2)? b) What is SD(X + Y + Z)?

Q: Let X, Y be independent Uniform (0, 2) random variables. Define Y, if X }. Z = Compute E[Z] and…

A: X,Y ~ Uniform(0,2) E(X) = E(Y) = 0+22=1 Var(X) = Var(Y) = (2-0)212=412=13 Z = Yif X <122Yif X≥12…

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A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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A: *answer:

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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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A: Fisrt find the marginal pmf of X

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A: GivenE(x)=1Var(x)=2E(y)=2Var(y)=2

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A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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Q: what is E[XY]?

A:

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A: Construct the PMF of X1X2, So, P(X1X2 = x) = P(X1=1, X2 = 1) +P(X1=-1, X2 = -1)    if x =1P(X1=-1,…

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A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

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A: Given that:

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Q: random variables with E(X) =2, E(Y)=3 ,V(X)=4,V(Y)=16. Find a)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y)…

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Q: .. Let X, Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X, Y) = 2,…

A: In question, Given that X, Y, Z are three random variables with mean mu and variance sigma^2. And…

Q: The mean of the random variable X is ux = 38 and the coefficient of variation is Vx=0.37. Let Z be…

A: Z = x - μσ