Analyzing Coin Toss Sequences: Runs, Child Mortality, and Chimps' Performance Insights
Join us in this engaging lecture as we explore the intriguing world of statistics through coin toss simulations. We'll start by determining the longest run of heads from a million tosses and experiment with R code to uncover insights. Additionally, we delve into global child mortality rates through comparative analysis and visual data representation using histograms. Learn about uncertainty in statistical data by simulating classes of chimps and their performance. Prepare for an interactive session filled with data collection and analysis!
Analyzing Coin Toss Sequences: Runs, Child Mortality, and Chimps' Performance Insights
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Presentation Transcript
Runs • Q: • Toss a coin 1000000 times. • Run is an unbroken sequence of H in a row • What is the length of the longest run • Take guesses (closest will get a cookie) • We will write an R code togather
Issues • Case sensitive dog and Dog are different • Careful of extra spaces • Brackets • ( ) • arguments of functions sum(coin); for(i in 1:10), if(coin<1) • grouping math formulas (1+3)*(4+5) • [ ] indexing valus in a list coin[10] • { } grouping commands togather
Are we smarter than chimps? • In each of the following pair one country has twice the child mortality rate than the other. • Malaysia or Russia • Poland or South Korea • Pakistan or Vietnam • Thailand or South Africa • Sri Lanka or Turkey
Answers • In each of the following pair one country has twice the child mortality rate than the other. • Malaysia or Russia • Poland or South Korea • Pakistan or Vietnam • Thailand or South Africa • Sri Lanka or Turkey • Collect data and draw a histogram
Chimps histogram plot(0:5,20*dbinom(0:5,5,.5),type="h",xlab="number of correct answers",ylab="average number of chimps")
What about uncertainty • 1000 classes of chimps simulated. • Classes ordered based on average performance • Will Show: Worst class, 2.5%, 5%, 25% nclass=1000 nchimps=20 nquestions=5 count1=matrix(0,nrow=nclass,ncol=nquestions+1) m1=rep(0,nclass) for (i in 1:nclass){ data1=rbinom(nchimps,nquestions,.5) count1[i,]=tabulate(data1,nquestions+1) m1[i]=mean(data1) } i1=order(m1) i2=order(count1[,1]) par(mfrow=c(2,2)) plot(0:5,count1[i1[1],],type="h",xlab="number of correct answers",ylab="average number of chimps",sub="1:1000") plot(0:5,count1[i1[25],],type="h",xlab="number of correct answers",ylab="average number of chimps",sub="25:1000") plot(0:5,count1[i1[50],],type="h",xlab="number of correct answers",ylab="average number of chimps",sub="50:1000") plot(0:5,count1[i1[250],],type="h",xlab="number of correct answers",ylab="average number of chimps",sub="250:1000")
