Mathematics for Computer Science
19.6. Sums of Random Variables 813 Algebra aside, there is a brilliant idea in this proof: in this context, exponenti- ating som ...
Chapter 19 Deviation from the Mean814 The second step relies on the inequality cv 1 C.c1/v; which holds for allvinŒ0;1çandc 1. ...
19.6. Sums of Random Variables 815 Chebyshev’s Theorem gives us the stronger result that PrŒjTExŒTçjcTç 1 c^2 : The Chernoff ...
Chapter 19 Deviation from the Mean816 Proof. PrŒTD0çDPrŒA 1 \A 2 \:::\Anç (T D 0 iff noAioccurs) D Yn iD 1 PrŒAiç (independence ...
19.7. Really Great Expectations 817 19.7.1 Repeating Yourself Here’s the bet: you make independent tosses of a fair coin until a ...
Chapter 19 Deviation from the Mean818 Problems for Section 19.1 Practice Problems Problem 19.1. The vast majority of people have ...
19.7. Really Great Expectations 819 temperature,T, of a cow as a random variable. Carefully specify the probability space on whi ...
Chapter 19 Deviation from the Mean820 Problems for Section 19.3 Practice Problems Problem 19.5. Suppose 120 students take a fina ...
19.7. Really Great Expectations 821 (c)Assume the outcomes of the card games are pairwise independent. What is the variance in t ...
Chapter 19 Deviation from the Mean822 Show that for any real number,, and real numbersx > 0, there is anRfor which the Che ...
19.7. Really Great Expectations 823 Homework Problems Problem 19.12. A man has a set ofnkeys, only one of which will fit the loc ...
Chapter 19 Deviation from the Mean824 Prove that the expected absolute deviation is always less than or equal to the stan- dard ...
19.7. Really Great Expectations 825 (a)Letmbe the probability that any given triangle,T, is monochromatic. Write a simple formul ...
Chapter 19 Deviation from the Mean826 (a)Apply the Chebyshev bound to the temperatureT of a random cow to show that at most 20% ...
19.7. Really Great Expectations 827 ŒBiDBjçthat happen wherei¤j. It was observed in Section 16.4 (and proved in Problem 18.2) th ...
Chapter 19 Deviation from the Mean828 a sequenceR 1 ;R 2 ;::: of pairwise independent random variables with the same mean and va ...
19.7. Really Great Expectations 829 Exam Problems Problem 19.24. You work for the president and you want to estimate the fractio ...
Chapter 19 Deviation from the Mean830 Mr. President, eitherpis within 0.04 of 0.53 or something very strange (5- in-100) has ha ...
19.7. Really Great Expectations 831 Given that the first two lines of code selected in therandom sampleare the same kind of sta ...
Chapter 19 Deviation from the Mean832 (b)What would the Markov bound be on the probability that the gambler will win at least 10 ...
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