Statistics324_HW3

# Statistics324_HW3 - mean(sim2) [1] 1.073524

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Statistics 324 – Discussion 311 w/ Jack Homework 3 – Victoria Yakovleva 1. xvals<-seq(from=-3, to=3, by=0.01) p<-pnorm(xvals) xyplot(p~xvals,type=c("l","g")) The cumulative distribution function is a continuous, increasing, sigmoidal shaped function that extends from p=0 to p=1. 2. al<-1-pnorm(100,96,14) al [1] 0.3875485 al^3 [1] 0.05820739 grain<-diff(pnorm(c(50,80),96,14)) grain [1] 0.1260403 qnorm(c(0.05,0.95),96,14) [1] 72.97205 119.02795

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3. 1-pexp(3.0,0.93) [1] 0.06142121 diff(pexp(c(1.0,3.0),0.93)) [1] 0.3331325 qexp(0.9,0.93) [1] 2.475898 4. sim<-rexp(100000,rate=0.93) mean(sim) [1] 1.071931 sim2<-rexp(100000,rate=0.93)
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Unformatted text preview: mean(sim2) [1] 1.073524 sim3&lt;-rexp(100000,rate=0.93) mean(sim3) [1] 1.069851 sim4&lt;-rexp(100000,rate=0.93) mean(sim4) [1] 1.069524 sim5&lt;-rexp(100000,rate=0.93) mean(sim5) [1] 1.076802 sim6&lt;-rexp(100000,rate=0.93) mean(sim6) [1] 1.074298 sim7&lt;-rexp(100000,rate=0.93) mean(sim7) [1] 1.072592 sim8&lt;-rexp(100000,rate=0.93) mean(sim8) [1] 1.072341 sim9&lt;-rexp(100000,rate=0.93) mean(sim9) [1] 1.070545 sim10&lt;-rexp(100000,rate=0.93) mean(sim10) [1] 1.076244 Theoretical Mean: 1/0.93 = 1.075269 Yes, the simulated means are close to the theoretical mean....
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## Statistics324_HW3 - mean(sim2) [1] 1.073524

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