Question

Question 10

RD 1 (X-μ)/μ|. Show that (5.28) 9. See Problem 5.8. Compute the signal-to-noise ratio r for the random variables from the fol. lowing distributions: (a) P(A), (b) E(n, p), (c) G(p), (d) Γ(α, β), (e) W (α, β), (f) LNue). and (g) P(α,0), where α > 2. 10. Let X and F be the sample means from two independent samples of size n from a popu- lation with finite mean μ and variance σ. Use the Central Limit Theorem (treating it as exact) to approximate the smallest value of n for which P(R-/ < σ/10) > .95. 11. We have noted that X, c implies that X, c. Show that the converse does not hold. (Hint: Consider discrete variables X, which take the values n and-n, each with probability qm 1/n, and is equal to zero otherwise. Show that x,马0, but that x, .) 2. We have noted that X, implies that X, X. Show that the converse does not hold. (Hint: Fix the positive integer k 2 1. Let U ~U(0, 1). For each positive integer n such that 2t-1 n < 2, let j = n-2t-1. Define Kn = 1U/(2k-1),(1+1)/(2k-y)(U) for j = 0,1 , . . . , 2k-1-1 Note that each X, is equal to 1 on a subinterval of [0, 1]; for n is such that 2-1 < n < 2k

Answer 1