What is Var[3X]? Let X be a random variable such that Var[X] = 5 and E[X] = 4.
What is Var[3X]? Let X be a random variable such that Var[X] = 5 and E[X]...
Let X be a random variable with E[X] = 2, Var(X) = 4. Compute the expectation and variable of 3 - 2X.
Problem 1. (a) Let X be a Binomial random variable such that E(X) 4 and Var(x) 2. Find the parameters of X (b) Let X be a standard normal random variable. Write down one function f(t) so that the random variable Y-f(X) is normal with mean a and variance b.
3. Let X be a continuous random variable with E(X)-μ and Var(X)-σ2 < oo. Suppose we try to estimate μ using these two estimators from a random sample X, , X,: For what a and b are both estimators unbiased and the relative efficiency of μι to is 45n?
3. (10 pts.) X is a Gaussian random variable with E{X} = 2 and Var(X) = 16. Let Y = 3X +1. Determine the probability: Pr(Y > 2)
Let x be a continuous random variable. Prove var(x) .
(assuming var(x) exist)
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
6. Let X be an exponential random variable with parameter 1 = 2. Compute E[ex]. = 7. Consider a random variable X with E[X] u and Var(X) 02. Let Y = X-4. Find E[Y] and Var(Y). The answer should not depend on whether X is a discrete or continuous random variable.
Consider two random variables, X and Y. Let E(X) and E(Y) denote the population means of X and Y respectively. Further, let Var(X) and Var(Y) denote the population variances of X and Y. Consider another random variable that is a linear combination of X and Y Z- 3X- Y What is the population variance of Z? Assume that X and Y are independent, which is to say that their covariance is zero.
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....
Consider a random variable X with the following properties E[X] = 20 and var(X) = 2. Consider a new random variable such that Y = 5 – 5X Calculate the following. (a) E[Y] = = (b) var(Y) = À