diff --git a/lab08.R b/lab08.R new file mode 100644 index 0000000..43026f6 --- /dev/null +++ b/lab08.R @@ -0,0 +1,86 @@ +# 2 +r <- 1 / 20 +qexp(0.5, rate = r) + +# 3a +r <- 1 / 20 +pexp(10, rate = r) + +#3b +r <- 1 / 20 +1 - pexp(15, rate = r) + +#3c +r <- 1 / 20 +pexp(10, rate = r) - pexp(5, rate = r) + +# 4 +set.seed(123) + +r <- 1 / 20 + +wait100 <- rexp(100, rate = r) +wait1000 <- rexp(1000, rate = r) +wait10000 <- rexp(10000, rate = r) + +par(mfrow = c(1, 3)) + +hist(wait100, + breaks = 20, + main = "Bus Waits (n = 100)", + xlab = "Waiting time (minutes)", + ylab = "Frequency") + +hist(wait1000, + breaks = 20, + main = "Bus Waits (n = 1000)", + xlab = "Waiting time (minutes)", + ylab = "Frequency") + +hist(wait10000, + breaks = 20, + main = "Bus Waits (n = 10000)", + xlab = "Waiting time (minutes)", + ylab = "Frequency") + +# 5 +set.seed(123) + +r <- 1 / 20 +waits <- rexp(10000, rate = r) +mean(waits < 10) + +#6a +pnorm(9.03, mean = 9.01, sd = 0.05) + +#6b +1 - pnorm(9.02, mean = 9.01, sd = 0.05) + +#6c +pnorm(9.1, mean = 9.01, sd = 0.05) - pnorm(8.9, mean = 9.01, sd = 0.05) + +#7a +qnorm(0.95, mean = 9.01, sd = 0.05) + +#7b +qnorm(0.05, mean = 9.01, sd = 0.05) + +#7c +qnorm(0.25, mean = 9.01, sd = 0.05) + +#8 +set.seed(123) + +mu <- 9.01 +sigma <- 0.05 + +b100 <- rnorm(100, mean = mu, sd = sigma) +mean(b100 >= 8.9 & b100 <= 9.1) + +b1000 <- rnorm(1000, mean = mu, sd = sigma) +mean(b1000 >= 8.9 & b1000 <= 9.1) + +b10000 <- rnorm(10000, mean = mu, sd = sigma) +mean(b10000 >= 8.9 & b10000 <= 9.1) + +pnorm(9.1, mean = 9.01, sd = 0.05) - pnorm(8.9, mean = 9.01, sd = 0.05) \ No newline at end of file