Let X-N (24,36) Y-N (48,64)
A) Find the expected value and the variance of x+2y
B)Find the probability that 2x+y > 50
Let X-N (24,36) Y-N (48,64) A) Find the expected value and the variance of x+2y B)Find...
Statistic problems an explanation would be appreciated(5pts) Let \(X \sim N(25,3)\). Find the expected value, variance, and standard deviation of\(X .\) Find \(P(X \leq 26.5)\)(5pts) Let \(X \sim N(12,2)\). Find the expected value, variance, and standard deviation of \(X\). Find \(P(X>12.8)\)(5pts) Let \(Y \sim\) binomial \((15, .65)\). Find the expected value, variance, and standard deviation of \(Y\). Find \(P(Y=10)\).
Let the expected value of random variable X be a, the expected value of Y be b, and the expected value of Z be c. Find E(4 − 2X + 3Y − 10Z).
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y have the moment generating function My (t) i. Show that the moment generating function of Z = aY b is e*My(at) for non-zero constants a and b ii. Use the result to write down the moment generating function of W 1- 2X if X Gamma(a, B)
(a) If var[X o2 for each Xi (i...
Let X N(0, 9) have mean 0 and variance 9. Find the expected value of X2(X +1).
Let X be Gaussian with zero mean and unit variance. Let Y = |X|. Find: a) The PDF fY (y) b) The mean E[Y ] c) Here X is uniform in (0, 1), but now you are asked to find a functiong(·) such that the PDF of Y = g(X) is ?2y 0≤y<1fY (y) = 0 otherwise
Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random variables with mhean μ and variance a) Compute the expected value of W b) For what value of a is the variance of W a minimum? σ: Let W-aX + (1-a) Y, where 0 < a < 1.
Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random...
E = "Expected Value"
V = "Variance"
0 < x < 00, x < y < oo IS joint probability density function a) Compute the probability that X < 1 and Y < 2. b) Find E(X) c) Find E(Y d) Find V(X) e) Find V(Y)
Let the variance of random variable X be 3, the variance of Y be 12, and the variance of Z be 9, and let X, Y , and Z be uncorrelated. Find V ar(4 − 2X + 3Y − 10Z).
Let X and Y be two independent and identically distributed random variables with expected value 1 and variance 2.56. First, find a non-trivial upper bound for P(|X + Y − 2| ≥ 1). Now suppose that X and Y are independent and identically distributed N(1,2.56) random variables. What is P(|X + Y − 2| ≥ 1) exactly? Why is the upper bound first obtained so different from the exact probability obtained?
Let Y-ar+b (a) Find the mean and variance of Y in terms of the mean and variance of X b) Evaluate the mean and variance ofY if Xhas the following PDF: (a)-ele (c) Evaluate the mean and variance of Y if Xis the Gaussian random variable with mean 0 and variance d) Evaluate the mean and variance of Yif X-bcos 2U) where U is a uniform random variable in of 1 the unit interval.
Let Y-ar+b (a) Find the mean...