Need statistics help with Chernoff Bound and Markov Bound

Statistics
Tutor: None Selected Time limit: 1 Day

 One night, there are 4 dozen free donuts upstairs. The 25 people in 271 are working on a midnight 61C deadline, and are each 30% likely to ignore the donuts. The 40 people in the other labs aren’t as stressed, but are each 10% likely to have already filled up on pizza (per midterm 2). Assume that everyone makes their decision independently.

Dec 1st, 2015

Thank you for the opportunity to help you with your question!

(a) A Chernoff bound for binomial variables that one can derive from the lecture states that for

 the sum of independent indicator variables with expectation µ and α ≥ 1 that Pr[X ≥ αµ] ≤

exp(αµ−µ−αµlnα

). Use this fact to bound the probability that there’ll be enough donuts for everyone

 (assuming, unrealistically, that no one takes seconds).

(b) Part a uses a form of Chernoff bound derived by applying the Markov bound to α

^X1+...+Xn

.You should use the inequality e

^x ≥ x+1


Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 1st, 2015

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