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by: Nick Rowe

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# Introduction To Simulation And Modeling Of Computer Systems CS 54300

Marketplace > Purdue University > ComputerScienence > CS 54300 > Introduction To Simulation And Modeling Of Computer Systems
Nick Rowe
Purdue
GPA 3.68

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
8
WORDS
KARMA
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## Popular in ComputerScienence

This 8 page Class Notes was uploaded by Nick Rowe on Saturday September 19, 2015. The Class Notes belongs to CS 54300 at Purdue University taught by Staff in Fall. Since its upload, it has received 55 views. For similar materials see /class/208099/cs-54300-purdue-university in ComputerScienence at Purdue University.

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Date Created: 09/19/15
Probability Theory Vs Statistics In Probability Theory we define a model and ask how objects quotbehavequot in that model In Statistics we observe quotbehaviorquot of objects and ask what is the quotlikelyquot model that explains this behavior Estimating a parameter Let p be the probability that a person will vote for candidate A We are interested in quotestimatingquot 19 using a sample of n randomly selected persons Let 1571 be the number of persons voting for A among the n persons Observing 1571 what can we say about 19 Definition 1 A 1 q confidence interval for a parameterT is an interval t1t2 such that PI T E t1t2 Z 1 q In our experiment we take a confidence interval 29 25 6256 ifFPlt25 5orpgt56 q VOteS 55L 6715 Bounding q Let p gt 15 6 The expected number of votes in that case is hp 2 7205 6 We need to find 6 such that 1571 g np1 e L 6 1 21 6 quot6 I Uz The probability of that event is bounded by q S np 23 S e gwwxl Testing Statistical Hypothesis A company applies for an FDA approval of a drug claiming that the drug performs better than known solutions or placebo Let p be the effective ratio of the new drug and p0 the effective ratio of previous treatments Two com peti ng hypothesis Horp povs H1rpgtpo The test n patients were treated with the new drug X7 1 ifF the treatment to patient 239 was successful else X7 O The decision procedure Accept H1 if gt C i1 else accept H0 Error Estimates Two types of errors 1 Type 1 error Accepting H1 when p g m The confidence level of the test or PrTypeIerr0r PrZ X7 gt 0 19 3 p0 7L1 2 Type II error Accepting H0 when p gt 190 The power of the test PrTypeIIerr0r PrZ Xi 3 Ch gt 190 71 Using ChernofF bound we can bound the probabilities of both events For a quotreasonablequot 04 ltlt 12 we need to take C gt 1 l enp0 Using this bound we get a S e np0623 But in that case for p 6 290290 26 is close to 1 19 needs to be significantly far from p0 for acceptance with small 04 and

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