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Commit c1ee67ff authored by Robert Ricci's avatar Robert Ricci

Copy in working notes

parent 545b87f9
Execution time:
Normally distributed - mean 5 seconds, sttdev 1 second
> dnorm: density, pnorm: distribution, qnorm: quantile
All: x, mean=, sd=
dnorm(5,mean=5,sd=1)
x <- seq(0, 10, by=.1)
plot(x,dnorm(x, mean=5, sd=1))
plot(x,pnorm(x, mean=5, sd=1))
XXX draw area under curve
XXX plot lines default?
Part A: probability of being more than 8s
pnorm(8, mean = 5, sd = 1) tells you prob of being 8 or less, so 1 -
Don't forget, probabilty, not percent
Part B: probability of being less than 6s
pnorm(6, mean = 5, sd = 1)
Part C: prob of being between 4 and 7
pnorm(7, mean = 5, sd = 1) - pnorm(4, mean = 5, sd = 1)
Part D: 95th percentile execution time
Inverting the PDF
qnorm(0.95, mean = 5, sd = 1)
> x = seq(0,1,by = 0.01)
> plot(x,qnorm(x,5,1))
Question 5:
D <- c(9, 11, 13, 14, 15, 15, 16, 19, 21, 23, 23, 23, 23, 24, 24, 25, 28, 28, 29, 31, 33, 33, 34, 34, 34, 35, 35, 36, 36, 38, 39, 42, 45)
A 10th and 90th percentiles
D[as.integer(length(D)*.10)]
D[as.integer(length(D)*.90)]
quantile(D,.90)
B mean
mean(D)
C 90% ci
mean(D) - (qnorm(.95)*sd(D))/sqrt(10)
D What fraction less than 25, and what is 90% CI for the fraction
XXX
E One-sided confidence interval 90%
Question 6:
c = concatenate
> A <- c(140, 120, 176, 288, 992, 144, 2736, 2796, 752, 17720, 96)
> B <- c(98, 120, 141, 317, 893, 86, 1642, 1678, 376, 8860, 67)
> D <- A - B
> mean(A)
> mean(B)
> mean(D)
X +- z*s / sqrt(n)
z_1-2/alpha
XXX / 2
XXX paired
XXX nonpaired
> plot(x,mean(D) - (qnorm(x)*sd(D))/sqrt(10), type='l',
> ylim=c(-1000,3000))
> lines(x,mean(D) + (qnorm(x)*sd(D))/sqrt(10))
mean(D) - (qnorm(0.9)*sd(D))/sqrt(10)
mean(D) + (qnorm(0.9)*sd(D))/sqrt(10)
(really 80%)
XXX diff
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