Sorry, I forgot to upload the Chernoff inequality function in this problem. Please take a look at it and give me a brief answer. It will due in three hours. Please write down anything you know. Any kind of answers would be helpful. Thank you!!!!

WLLN vs CLT and Large vs Small Deviations A stronger version (called Berry-Esseen Theorem) of CLT states that if X1, X2, ..., Xn are independent and identically distributed random variables with zero mean and unit variance and E[X,|3] = 3, then for all r and n we have [Fr(x) - D(x)| 0.47483 Vn 2, where Fr(.) is the CDF of - _ Xi, and o(.) is the CDF of the zero-mean and unit-variance Gaussian random variable. The said bound is due to Irina Shevtsova. 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) developed in HW 6, Prob. 7 for m > 500. . Find an upper bound Bm on Pm in terms of o(.) based on Berry-Esseen Theorem (CLT) stated above for m > 500. . Plot the two bounds as a function of m for in the range from 501 to 600. Which bound is better in what region?Consider Chernoff inequality. (a) Let X1, X2, ..., Xn denote n independent Bernoulli random variables with parameter p. Let Z = _ _, Xi. Use Chernoff inequality and show the following for any 8 > 0: P(Z > p+8)