Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

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

We have the following information regarding the random variables X, X, and X3: Var(X1) = Var(X2) = Var(X3), Px, X2 = 0.2, pxX, = 0.5, px X Calculate the correlation between X+ X3 and X2 + X3. (i.e. calculate px+Xs.X2+X3) 0.9. %3D

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