Problem 10: A random variable X has a characteristic function x(w) = j (2w + w²). If you are given that fox2fx (x)dx = 9. Find the variance of the RV Y = 2x-2. Find the variance of Y

Imagine a family member looks over your shoulder as you look at the variance equation Σki=1(xi − μ)2P(X = xi) and asks why the P(X = xi) term is there. What would you say?

Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter ) > 0 and density 1 f(x; A) = x > 0. Consider the following two estimators of X: 3 1 ΣΧ, Ã = nX(1). 3 i=1

Let M₁ (2) and M₂(z) be the m.g.f. of r.v.'s X₁ and X2, respectively. Suppose that M (0) = M₂(0) and M"(0) > M"(0). Which of the following statements is true? The mean of X₁ is greater than the mean of X₂ The variance of X₁ is equal to the variance of X₂. The variance of X₁ is greater than the variance of X₂. The variance of X₁ is less than the variance of X₂

when using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?