If X ∼ Poisson(3) and Y |X = k ∼ χ2 (2k + 1), then Var (Y ) =
Suppose that X ~ χ2(m), Y-2(n), and X and Y are independent. Is Y-X ~ χ2 if
X is a Poisson random variable of parameter 3 and Y an exponential random variable of parameter 3. Suppose X and Y are independent. Then A Var(2X + 9Y + 1) = 22 B Var(2X + 9Y + 1) = 7 CE[2X2 + 9Y2] = 19 D E[2X2 + 9Y2] = 26
k=0 Q3 Suppose X has Poisson(1) distrubution. Calculate the following (a) Determine P(X = k) for k E No = {0, 1, 2, ..., n, ...}. [1] (b) Evaluate Ź P(X = k). [1] (c) Determine E(X). [1] (d) Determine E(X(X – 1)). [2] (e) Use the result in (d) to calculate E(X). [1] (f) Calculate Var(X). [1] (g) Calculate Eſax). [3] (h) Calculate Var(a*). [3] (i) Determine E (1+x). [2]
Given Var(X) = 4, Var(Y) = 1, and Var(X+2Y) = 10, What is Var(2X-Y-3)? I know the answer is 15, I'm particularly interested in the specific steps involved with finding the cov(X,Y) in this problem. Please explain in detail, step by step how you come to cov(X,Y) = 0.5 in this equation. Please include any formulas you would need to use to find the cov(X,Y) in this equation.
X,Y, and Z are random variables. Var(X) = 2, Var(Y) = 1, Var(Z) = 5, Cov(X,Y) = 3, Cov(X, Z) = -2, Cov(Y,Z) = 7. Determine Var(3X – 2Y - 2+10)
Prove, Var(ay)= a^2 var(y) Var(y+a)= var(y) Var(x+y)= var(x)+var(y)+2cov(x,y)
6 Suppose that X and Y are random variables such that Var(X) Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y+2)
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
Suppose XX and YY are independent random variables for which Var(X)=7Var(X)=7 and Var(Y)=7.Var(Y)=7. (a) Find Var(X−Y+1).Var(X−Y+1). (b) Find Var(2X−3Y)Var(2X−3Y) (c) Let W=2X−3Y.W=2X−3Y. Find the standard deviaton of W.W.
Suppose X ~ Poisson(2λ) & Y ~ Poisson(3λ) are independent. Show that T = (.32)X + (.12)Y is an unbiased estimator of λ & determine Var(T). Hint: begin by computing E(T).