WLLN vs CLT and Large vs Small Deviations A fair coin is tossed 1000 times. Let Pm denote the probability of observing more than m HEADS. Find an upper bound Am on Pm based on the Chernoff Inequality (WLLN) for m > 500. Find an upper bound Bm on Pm in terms of () based on Berry-Esseen Theorem (CLT) for m > 500. Plot the two bounds as a function of m for in the range from 501 to 600. Also plot the actual probability using a computer. Which bound is better in what region?