Chebyshev's Inequality and Central Limit Theorem Suppowe we toss a fair die 100 times. Let {X}100 denote the draws, wher

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Chebyshev S Inequality And Central Limit Theorem Suppowe We Toss A Fair Die 100 Times Let X 100 Denote The Draws Wher 1 (29.67 KiB) Viewed 18 times

Chebyshev's Inequality and Central Limit Theorem Suppowe we toss a fair die 100 times. Let {X}100 denote the draws, where Px,(k:) = 1/6 for k = 1,..., 6. Now let 100 Υ - ΣΧ, denote the empirical sum of the draws. a. Find E[X) and Var(X). b. Use the Chebyshev inequality to bound the probability that the sum (over 100 tosses) is between 300 and 400, i.e., P{300 < Y S 400}. c. Use the Central Limit Theorem to approximate the probability that the sum (over 100 tosses) is between 300 and 400, i.e., P{300 SY < 400}. Hint: You might want to look at the Q function table included at the end. d. Compare the two results above.