Suppose that X ~ χ2(m), Y-2(n), and X and Y are independent. Is Y-X ~ χ2...
Suppose X ~N(0,9) and Y ~N(1,16) X and Y are independent, then P(0<X+Y<2) =
Suppose X, Y are independent and X~N(1,4) and Y N(1,9). If P(2X Y a) P(4X - 2Y 2 4a), then find a
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X) < Var(Y) SupposeX-N(Aof) and Y-N(H2,σ ), they arc indcpcndcnt, thcn in the following statementss incorrect 4) 5) Suppose X~NCHiof) and Y~NCHz,σ ), they are independent, if PCIX-Hik 1) > PCIY _ μ2I 1), then ( ) is correct.
Suppose X, Y are independent with X ∼ N (0, 1) and Y ∼ N (0, 1). Show that the distribution of Q = X/Y follows the Cauchy distribution, i.e., f(q) = 1/π(1+q2) . Hint: Let Q = X/Y and V=Y. Find the joint pdf of Q and V and finally find the marginal pdf of Q by integrating the joint pdf of Q and V w.r.t. V: Y π(1+q2) Y V = Y . Find the joint pdf of...
5. Suppose that X and Y are independent with distributions N(0,0) and N(0,02), respectively. Let Z=X+Y. Also, let W = 02X – oʻY. Prove that Z and W are uncorrelated.
5)Suppose that X ∼ N(-1.9,2.7), Y ∼ N(3.5,1.4), and Z ∼ N(1.2, 1.0) are independent random variables. Find the probability that 2.2X + 3Y + 4Z ≥ 8.8. Round your answer to the nearest thousandth. 6) Suppose that X ∼ N(-2.0,2.6), Y ∼ N(3.0,2.0), and Z ∼ N(1.7, 0.5) are independent random variables. Find the probability that |3.1X + 3Y + 4Z| ≥ 8.0. Round your answer to the nearest thousandth.
Suppose that we have two independent binomial random variables X ~Binomial(n, px) and Y ~ Binomial(m,Pv). You can assume that the MLE's are -X/n and p,-Y/m. (a) Find the MLE for p under the assumption that p (b) Find the LRT statistic T for testing p,-py HA:p.Ру vs. (c) Evaluate the value of this statistic if n 353, X 95, m -432, and Y 123. (d) Compare the answer from part (c) to a critical value from a x2 with...
is independent of X, and e Problem 3 Suppose X N(0, 1 -2) -1 <p< 1. (1) Explain that the conditional distribution [Y|X = x] ~N(px, 1 - p2) (2) Calculate the joint density f(x, y) (3) Calculate E(Y) and Var(Y) (4) Calculate Cov(X, Y) N(0, 1), and Y = pX + €, where
Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If X Exp(B = 1) and Y~ Unif(-1,1], what is the density of Z?
Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If X ~ Exp(B = 1) and Y~ Unif(-1,1], what is the density of Z?