QUESTION 4 Let X, Y be joint Gaussian random variables with E[X]=0,E[Y]=0, Var[X]=2, Var[Y] =4 and Cov[X, Y] =2. Compute E[XIY=1] as a decimal and enter the answer.

Q: Let X be a random variable such that E(X²) a. V(3x-3) b. E(3x-3) = 58 and V(X) = 40. Compute

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Q: Calculate E(X)

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Q: Suppose X and Y are random variables with E[XY ] = 6, E[Y ] = 4 and E[X] = 5 Find Cov(X; Y )

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Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

Q: 5. Let Y,, Y2, ., Yn be independent, exponentially distributed random variables with mean 0/2. Show…

A: Solution

Q: Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) = 10. We do not…

A: The provided information is as follows:. and  are independent random variables..

Q: QUESTION 2 Consider the following information about 3 random variables, X Y and Z. X|Y- Gamma(2Y2,).…

A: Given: X/Y ~ Gamma( 2Y2, Y) Y~ N(2, 5) From given: E(X/Y)=2Y2Y Var(X/Y)=2Y2Y2 We know that for…

Q: Suppose X and Y are independent random variables with expected values E[X] = 0, E[Y] = 0, and Var(X)…

A: We have given that  X and Y are independent random variables with expected values E[X] = 0, E[Y] =…

Q: QUESTION 2 Consider the following information about 3 random variables, X, Y and Z. X|Y-Gamma(2 Y2,…

A: Given: X/Y ~ Gamma(2Y2, Y) Y~ N(2, 5)   E(X/Y)=2Y2Y=2Y

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.2, an

A: Given information: Var(X)=1.6 Var(Y)=1.2 Cov(X,Y)=0.6 Let  Z = -1.2X + 1.9Y + 4.2.

Q: Let us say that we have jointly distributed random variables X and Y with E(X) = 3, E(Y) = 5, Var…

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Q: 66. Consider two random variables X and Y with V(X) = 5, V(Y) = 10 and Cov(X,Y) = 3. (a) Find V(3X -…

A: V(X)=5 , V(Y)=10 and Cov(X,Y)=3

Q: Let X be a random variable. Find E(Y) where 3 Y = (X – E(X)) (a) 1 (d) Q (b) 3/4 (e) -1 (с) —3/4 -

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Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: Let Y₁, Y2,..., Yn denote a random sample of size n from a population with a uniform distribution on…

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Q: Let Xi and Yi be random variables with Var(Xi) = σx2 and Var(Yi) = σy2 for all i ∈ {1, . . . , n}.…

A: It is given that: varxi=σx2varyi=σy2 and xi and yi are independent and corrxi,yi=ρ

Q: obtain the MVB estimator for u in normal population. №.(402), where 2 is know

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Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show…

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Q: Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a})…

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Q: Is cov(X, Y) random?

A: Given :Is cov(X, Y) random?

Q: A discrete random variable X can only take the values -1, 0 and 1. The probabilities of this are P(X…

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Q: what is E[XY]?

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Q: If x and y are independent random variable with E(xy)= 20 then the correlation coefficient is

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Q: 3. Suppose X and Y are two independent Gamma random variables: X~ Y Gamma(2, B = 1), where the first…

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Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: If X1 and X2 are independent random variables with distribution given by P[Xi] = −1 = P[Xi = 1] =…

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,…

Q: Let V=X+Y and U=X-Y are random variables, then the condition which make the covariance

A: Given that V=X+Y and U=X-Y are random variables. Formula for covariance between U and V is…

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…

Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: Let X1,X2,· · ,Xn be i.i.d. random variables, where X; ~ Bernoull Y1 = X1X Y, = X2X %3D Yn-1 = X_ Yn…

A: A random variable X is called to follow the Bernoulli distribution if it takes only non-negative…

Q: Let X1, X2, X3 be random variables each having a mean u and variance o'. Further, Cov(X1 X2) 2,…

A: The mean of a constant is equal to the value of the constant and the mean of sum of random variables…

Q: Let X, Y and Z be three independent random variables such that E(X)-E(Y)=E(Z)=1 and…

A: Solution: Given, E(X)=E(Y)=E(Z)=1 E(X^2)=E(Y^2)=E(Z^2)=10

Q: X and Y are discrete random variables. If var(X)= var(Y) = o², cov(X,Y)= find var(2X-3Y)

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Q: Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y +…

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