# fditraglia/Econ103Public

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0fe59a8 Mar 19, 2017
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 ## ----quadratic_plot------------------------------------------------------ x <- seq(from = -1, to = 1, by = 0.5) y <- x^2 plot(x, y) ## ----quadratic_plot_denser----------------------------------------------- x <- seq(from = -1, to = 1, by = 0.1) y <- x^2 plot(x, y) ## ----quadratic_plot_dense------------------------------------------------ x <- seq(from = -1, to = 1, by = 0.01) y <- x^2 plot(x, y) ## ----plot_type_line------------------------------------------------------ plot(x, y, type = "l") ## ----exercise_1---------------------------------------------------------- x <- seq(from = -2, to = 2, by = 0.01) y <- x^3 plot(x, y, type = 'l') ## ----exercise_2---------------------------------------------------------- x <- seq(from = 0.5, to = 1.5, by = 0.01) y <- log(x) plot(x, y, type = 'l') ## ----exercise_3---------------------------------------------------------- x <- seq(from = 0, to = 6 * pi, by = 0.01) y <- sin(x) plot(x, y, type = 'l') ## ----points-------------------------------------------------------------- x <- seq(from = 0, to = 1, by = 0.01) y1 <- x^2 y2 <- x plot(x, y1, col = 'blue', type = 'l') lines(x, y2, col = 'red') ## ----lines_fail---------------------------------------------------------- x <- seq(from = 0, to = 1, by = 0.01) y1 <- x^2 y2 <- x + 0.75 plot(x, y1, col = 'blue', type = 'l') lines(x, y2, col = 'red') ## ----cbind_matplot------------------------------------------------------- y <- cbind(y1, y2) y matplot(x, y, type = 'l') ## ----matplot_options----------------------------------------------------- y <- cbind(y1, y2) matplot(x, y, type = 'l', col = c("red", "blue"), lty = 1) ## ----exercise_4---------------------------------------------------------- x <- seq(from = 0, to = 2 * pi, by = 0.01) y1 <- sin(x) y2 <- cos(x) y3 <- 2 * sin(x + pi/4) y <- cbind(y1, y2, y3) matplot(x, y, type = 'l', col = c("black", "red", "blue"), lty = 1) ## ----rbinom-------------------------------------------------------------- rbinom(20, size = 10, prob = 1/2) ## ----rbinom_moments------------------------------------------------------ sims <- rbinom(100000, size = 10, prob = 1/2) mean(sims) - (10 * 1/2) var(sims) - (10 * 1/2 * 1/2) ## ----exercise_5---------------------------------------------------------- sims <- rbinom(100000, size = 20, prob = 0.9) mean(sims) - (20 * 0.9) var(sims) - (20 * 0.1 * 0.9) ## ----dbinom-------------------------------------------------------------- dbinom(7, size = 10, prob = 0.8) choose(10, 7) * (0.8)^7 * (0.2)^3 ## ----dbinom_full_support------------------------------------------------- support <- 0:10 p.x <- dbinom(support, size = 10, prob = 0.5) p.x ## ----plot_binomial_density----------------------------------------------- plot(support, p.x) ## ----plot_type_h--------------------------------------------------------- plot(0:10, p.x, type = 'h', xlab = 'x', ylab = 'p(x)', main = 'pmf for a Bernoulli(n = 10, p = 0.5) RV') ## ----exercise_6---------------------------------------------------------- support <- 0:20 p.x <- dbinom(support, size = 20, prob = 0.65) plot(support, p.x, type = 'h', xlab = 'x', ylab = 'p(x)', main = 'pmf for a Bernoulli(n = 20, p = 0.65) RV') ## ----pbinom-------------------------------------------------------------- sum(dbinom(0:7, size = 20, prob = 0.3)) pbinom(7.4, size = 20, prob = 0.3) ## ----exercise_7---------------------------------------------------------- sum(dbinom(0:24, size = 50, prob = 0.5)) pbinom(24.5, size = 50, prob = 0.5) ## ----plot_pbinom--------------------------------------------------------- x <- seq(from = -1, to = 10, by = 0.01) y <- pbinom(x, size = 10, prob = 0.5) plot(x, y, ylab = 'F(x)') ## ----plot_type_s--------------------------------------------------------- plot(x, y, ylab = 'F(x)', type = 's') ## ----exercise_8---------------------------------------------------------- x <- seq(from = -1, to = 21, by = 0.01) y1 <- pbinom(x, size = 20, prob = 0.2) y2 <- pbinom(x, size = 20, prob = 0.5) y3 <- pbinom(x, size = 20, prob = 0.8) y <- cbind(y1, y2, y3) matplot(x, y, col = c("black", "blue", "red"), type = 's', lty = 1, ylab = "F(x)") ## ----exercise_9---------------------------------------------------------- #Part 1 plot(0:20, dbinom(0:20, size = 20, prob = 0.5), type = 'h', ylab = 'p(x)') #Part 2 sum(dbinom(12:20, size = 20, prob = 0.5)) #Part 3 sum(dbinom(18:20, size = 20, prob = 0.5)) #Part 4 250 * sum(dbinom(12:20, size = 20, prob = 0.5)) 250 * sum(dbinom(18:20, size = 20, prob = 0.5)) ## ----exercise_10--------------------------------------------------------- #Binomial(n = 200, p) random variable where p is the unknown proportion who prefer boxers. 1-sum(dbinom((200*.45+1):(200*.65-1),size=200,p=.5)) ## ----exercise_11--------------------------------------------------------- #Exercise 11-1 n <- 10000 sim1 <- rpois(n, lambda = 1) sim5 <- rpois(n, lambda = 5) sim10 <- rpois(n, lambda = 10) sim15 <- rpois(n, lambda = 15) #Exercise 11-2 mean(sim1) mean(sim5) mean(sim10) mean(sim15) #Exercise 11-3 var(sim1) var(sim5) var(sim10) var(sim15) #Exercise 11-4 range(sim1) table(sim1) range(sim5) table(sim5) range(sim10) table(sim10) range(sim15) table(sim15) #Exercise 11-5 x <- -1:15 plot(x, dpois(x, lambda = 2), type = 'h', ylab = 'p(x)') plot(x, ppois(x, lambda = 2), type = 's', ylab = 'F(x)')