Solution :
E(X) = 2
V(X) = 3
a)
b)
(1 point) For a random variable X, suppose that E[X] = 2 and Var(X) = 3....
(1 point) Para una variable aleatoria X, supongamos que E[X] = 5 y Var(X) = 10. entonces (a) E[( 5 x)?] = (b) Var(2 + 6X) =
Suppose A B C be random variable with E[A] = 3 and E [A^2]= 10 Var[B] = 5, E[C] = 2 E [c^2] = 7 we know A and B are independent E[AC] = 5 Cov(B, C) = 2 please find Var[3A +B - C]
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?
Recall that the variance of a random variable is defined as
Var[X]=E[(X−μ)2], where μ = E[X]. Use the properties of
expectation to show that we can rewrite the variance of a random
variable X as Var [X]=E[X^2]−(E[X])^2
Problem 3. (1 point) Recall that the variance of a random variable is defined as Var X-E(X-μ)21, where μ= E[X]. Use the properties of expectation to show that we can rewrite the variance of a random variable X as u hare i- ElX)L...
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
Question 2 0/1 point (graded) Now suppose that you have a random variable X, where E[X = 6 and Var [X= 2. The probability that X is greater than 11 or less than 1 is no more than
Please answer both.
. Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
5. Suppose X and Y are random variables such that E(X)=E(Y) = θ, Var(X) = σ and Var(Y)-吆 . Consider a new random variable W = aX + (1-a)Y (a) Show that W is unbiased for θ. (b) If X and Y are independent, how should the constant a be chosen in order to minimize the variance of W?
What is Var[3X]? Let X be a random variable such that Var[X] = 5 and E[X] = 4.
Consider a random variable X with the following properties E[X] - 10 and var(X) - 9. Consider a new random variable such that Y-1-5X Calculate the following (a) EY] - (b) var(Y) = 5