This paper concentrates on the primary theme of PROVE MILL’S INEQUALITY, THEOREM 4.7. HINT. NOTE THAT P(|Z| > T) = 2P(Z>T). NOW WRITE OUT.. in which you have to explain and evaluate its intricate aspects in detail. In addition to this, this paper has been reviewed and purchased by most of the students hence; it has been rated 4.8 points on the scale of 5 points. Besides, the price of this paper starts from £ 40. For more details and full access to the paper, please refer to the site.
5. Prove Mill’s inequality, Theorem 4.7. Hint. Note that P(|Z| > t) = 2P(Z>t). Now write out what P(Z>t) means and note that x/t > 1 whenever x>t. 6. Let Z ~ N(0, 1). Find P(|Z| > t) and plot this as a function of t. From Markov’s inequality, we have the bound P(|Z| > t) = E|Z| k tk for any k > 0. Plot these bounds for k = 1, 2, 3, 4, 5 and compare them to the true value of P(|Z| > t). Also, plot the bound from Mill’s inequality. 4.5 Exercises 69 7. Let X1,…,Xn ~ N(0, 1). Bound P(|Xn| > t) using Mill’s inequality, where Xn = n-1 n i=1 Xi. Compare to the Chebyshev bound