Suppose that X1 and X2 are two random variables. Suppose that X1 has mean 1 and...

Suppose that X1 and X2 are two random variables. Suppose that X1 has mean 1 and variance 4 while X2 has mean 3 and variance 9. Finally, suppose that the correlation between X1 and X2 is 3/8. Denote Y = 2X1 − X2. (67) The mean of Y is (a) 1 (b) 4 (c) -2 (d) -1 (68) The variance of Y is (a) 25 (b) 4 (c) 9 (d) 16 (69) The standard deviation of Y is (a) 5 (b) 2 (c) 3 (d) 4 (70) The correlation between X1 and Y is (a) 0 (b) 23/32 (c) 16/9 (d) 1 i need a clear, thorough answer to question 70 please.

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orchestra answered 1 year ago

X1 and X2 are two independent random variables that have Poisson distributions with mean lambda1 and...

X1 and X2 are two independent random variables that have Poisson distributions with mean lambda1 and lambda2, respectively. a) Use moment generating functions, derive and name the distribution of X = X1+X2 b) Derive and name the conditional distribution of X1 given that X = N where N is a fixed positive integer. Please explain your answer in detail. Please don't copy other answers. Thank you; will thumb up!

Suppose X1, X2, . . . are a sequence of iid uniform random variables with probability...

Suppose X1, X2, . . . are a sequence of iid uniform random variables with probability density function f(x) = 1 for 0 < x < 1, or 0, otherwise. Let Y be a continuous random variable with probability density function g(y) = 3y2 for 0 < y < 1, or 0, otherwise. We further assume that Y and X1, X2, . . . are independent. Let T = min{n ≥ 1 : Xn < Y }. That is, T...

X1 and X2 are two discrete random variables. The joint probability mass function of X1 and...

X1 and X2 are two discrete random variables. The joint probability mass function of X1 and X2, p(x1,x2) = P(X1 = 1,X2 = x2), is given by p(1, 1) = 0.025, p(1, 2) = 0.12, p(1, 3) = 0.21 p(2, 1) = 0.18, p(2, 2) = 0.16, p(2, 3) = c. and p(x1, x2) = 0 otherwise. (a) Find the value of c. (b) Find the marginal probability mass functions of X1 and X2. (c) Are X1 and X2 independent?...

Let X1, X2, . . . , Xn be iid Poisson random variables with unknown mean...

Let X1, X2, . . . , Xn be iid Poisson random variables with unknown mean µ 1. Find the maximum likelihood estimator of µ 2.Determine whether the maximum likelihood estimator is unbiased for µ

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2 = X1 −X2, Y3 =X1 −X3. Find the joint pdf of Y = (Y1,Y2,Y3)′ using : Multivariate normal distribution properties.

Suppose X1, X2, . . ., Xn are iid Poisson random variables with parameter λ. (a)...

Suppose X1, X2, . . ., Xn are iid Poisson random variables with parameter λ. (a) Find the MVUE for λ. (b) Find the MVUE for λ 2

1. Consider the following weighted averages of independent random variables X1, X2, X3, all with mean...

1. Consider the following weighted averages of independent random variables X1, X2, X3, all with mean u and variance σ^2 θ1 = 1/3(X1) + 1/3(X2) + 1/3(X3) θ2 = 1/4(X1) + 2/4(X2) + 1/4(X3) θ3 = 2/5(X1) + 2/5(X2) + 2/5(X3) a) Find E[θ1], E[θ2], E[θ3] b) Are θ1, θ2 and θ3 unbiased for u? Explain c) Find the variance for θ1, θ2 and θ3 d) If you had to use one of the above estimators, which would you pick?...

Consider independent random variables X1, X2, and X3 such that X1 is a random variable having...

Consider independent random variables X1, X2, and X3 such that X1 is a random variable having mean 1 and variance 1, X2 is a random variable having mean 2 and variance 4, and X3 is a random variable having mean 3 and variance 9. (a) Give the value of the variance of X1 + (1/2)X2 + (1/3)X3 (b) Give the value of the correlation of Y = X1- X2 and Z = X2 + X3.

Suppose that X1 and X2 are independent continuous random variables with the same probability density function...

Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x)= x/2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2, ). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y ).

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1...

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1 X2 = 2θ + ε2 X3 = 3θ + ε3 ε1, ε2, ε3 are independent and the mean and variance are the following random variable E(ε1) = E(ε2) = E(ε3) = 0 Var(ε1) = 4 Var(ε2) = 6 Var(ε3) = 8 What is the Best Linear Unbiased Estimator(BLUE) when estimating parameter θ from the three samples X1, X2, X3

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