# Likelihood and Examining Hypothesis and the Budgetary Bootstrap Devices (Section 1)

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The birthday issue (a not all that undeniable issue) Random variables and ... individuals aimlessly what is the likelihood that two or more have the same birthday? ...

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﻿FIN285a: Section 2.2.2 Fall 2010 Probability and Sampling Theory and the Financial Bootstrap Tools (Part 1)

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Sampling Outline (1) Sampling Coin flips The birthday issue (a not all that undeniable issue) Random factors and probabilities Rainfall The portfolio (precipitation) issue

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Financial Bootstrap Commands test number extent quantile histogram products

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Software finboot coinflip.m birthday.m portfolio1.m portfolio2.m

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Sampling Classical Probability/Statistics Random factors originate from static all around characterized likelihood circulations or populaces Observe just specimens from these populaces Example Fair coin: (0 1) (1/2 1/2) populaces Sample = 10 draws from this coin

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Old Style Probability and Statistics Try to make sense of properties of these specimens utilizing math equations Advantage: Precise/Mathematical Disadvantage Complicated recipes For moderately complex issues turns out to be exceptionally troublesome

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Bootstrap (resample) Style Probability and Statistics Go to the PC (finboot tool stash) Example coin = [ 0 ; 1] % heads tails flips = sample(coin,100) flips = sample(coin,1000) nheads = count(flips == 0) ntails = count(flips == 1);

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Sampling Outline (1) Sampling Coin flips The birthday issue (a not all that conspicuous issue) Random factors and probabilities Rainfall A first portfolio issue

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The Coin Flip Example What is the possibility of getting less than 40 heads in a 100 flips of a reasonable (50/50) coin? Could utilize likelihood hypothesis, however we'll utilize the PC This is an exemplary binomial conveyance (see Jorion 2.4.5) The PC is not so much vital for this issue

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Coin Flip Program in Words Perform 1000 trials Each trial Flip 100 coins Write down what number of heads Summarize Analyze the dissemination of heads Specifically: Fraction < 40

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Now to the Computer coinflip.m and the matlab proofreader

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Sampling Outline (1) Sampling Coin flips The birthday issue (a not all that undeniable issue) Random factors and probabilities Rainfall A portfolio issue

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Birthday If you draw 30 individuals indiscriminately what is the likelihood that at least two have a similar birthday?

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Birthday in Matlab Each trial days = sample(1:365,30); b = multiples(days); z(trial) = any(b>1) extent (z == 1) on to code

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Sampling Outline (1) Sampling Coin flips and political surveys The birthday issue (a not all that undeniable issue) Random factors and probabilities Rainfall A portfolio issue

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Adding Probabilities: Rainfall Example dailyrain = [80; 10 ; 5 ] probs = [0.25; 0.5; 0.25]

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Sampling annualrain = sum(sample(dailyrain,365,probs))

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Portfolio Problem Distribution of arrangement of size 50 Return of every stock [ - 0.05; 0.0; 0.10] Prob(0.25,0.5,0.25) Portfolio is similarly weighted on to matlab code (portfolio1.m)

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Portfolio Problem 2 1 Stock Return [-0.05; 0.05] with likelihood [0.25; 0.75] Probabilities of keeps running of positives 5 days of positive returns 4/5 days of positive profits for to matlab code portfolio2.m

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Sampling Outline (1) Sampling Coin flips The birthday issue (a not all that conspicuous issue) Random factors and probabilities Rainfall The portfolio (precipitation) issue