lab08

lab08.R

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+# 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)