07 Estimates - Pdf / Cdf Review Discrete and Continuous...

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Pdf / Cdf Review Discrete and Continuous Distributions A brief review
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0123456789 1 0 0.0 0.10 0.20 1 0 0.2 0.4 0.6 0.8 1.0 x n x k x x n x p p x n p n k X P p p x n p n x X P = = = = ) 1 ( ) , | ( ) 1 ( ) , | ( 0 Binomial Distribution
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Code for Binomial Plot ± n = 10 ± p = 0.7 ± x = seq(0,10,by=1) ± P2x = dbinom(x,n,p) ± cumulativeP2x = pbinom(x,n,p) ± par(mfrow=c(2,1)) ± barplot(P2x,names=as.character(x)) ± barplot(cumulativeP2x,names=as.character(x)) ± par(mfrow=c(1,1))
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-3 -2 -1 0 1 2 3 0.0 0.2 0.4 -3 -2 -1 0 1 2 3 0.6 = = = k x x dx e k X P e x X f 2 2 2 2 2 ) ( 2 2 ) ( 2 2 1 ) , | ( 2 1 ) , | ( σ μ πσ σμ Gaussian Distribution
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Code for Normal Plot ± n = 10 ± p = 0.7 ± x = seq(-3,3,by=.1) ± P2x = dnorm(x) # Note, mean=0,sd=1 ± cumulativeP2x = pnorm(x) ± par(mfrow=c(2,1)) ± plot(x,P2x,type='l',lwd=3,cex=2) ± plot(x,cumulativeP2x,type='l',lwd=3,cex=2) ± par(mfrow=c(1,1))
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Estimates and confidence intervals with one sample D & B Chapters 7.1, 8
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Gregor Mendel’s Genetics Experiment ± Crossing green peas with yellow peas. ± Expected 25% of offspring would be yellow. He got 26.2%. Good enough? ± 152 peas with yellow pods ± 428 peas with green pods ± 580 peas in total ± What we are looking at here is a proportion, but we will approximate it with a normal distribution…
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Notation for proportions ± Proportion of successes in the entire population: ± Sample proportion of x successes in a sample of size n: ± Sample proportion of failures in a sample of size n: p ˆ p q ˆ 1 ˆ = p
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When can we use a normal distribution to approximate a binomial? ± Sample is a simple random sample. ± We are drawing from a binomial distribution, i.e. two categories, independent trials, all with probability p of success. ± If np>=5 and nq>=5 then binomial can be approximated by a normal.
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A few definitions ± A point estimate is a single value or point used to approximate a population parameter ±
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell University (Engineering School).

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07 Estimates - Pdf / Cdf Review Discrete and Continuous...

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