# Need statistics help with Chernoff Bound and Markov Bound

*label*Mathematics

*timer*Asked: Dec 1st, 2015

*account_balance_wallet*$5

### Question Description

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.

## Tutor Answer

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.

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