CS计算机代考程序代写 ## —-echo=FALSE———————————————————-

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set.seed(2331)

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theta <- 0.5 x1.simulated <- numeric(1000) # initialise an empty vector for (i in 1:1000) { x <- runif(3, theta - 0.5, theta + 0.5) x1.simulated[i] <- min(x) } g <- function(x) 3 * (1 - x)^2 hist(x1.simulated, breaks = 20, freq = FALSE, col = "lightblue", xlim = c(0, 1), ylim = c(0, g(0)), main = NULL, xlab = expression(x[(1)])) curve(g, from = 0, to = 1, add = TRUE, col = "blue", lwd = 2) ## ------------------------------------------------------------------------ w.simulated <- matrix(nrow = 100, ncol = 3) # initialise an empty matrix for (i in 1:100) { x <- runif(3, theta - 0.5, theta + 0.5) x <- sort(x) w1 <- mean(x) w2 <- x[2] w3 <- (x[1] + x[3]) / 2 w <- c(w1, w2, w3) w.simulated[i, ] <- w } ## ------------------------------------------------------------------------ # Compute `mean` and `var` for each column of `w.simulated`. means <- apply(w.simulated, 2, mean) vars <- apply(w.simulated, 2, var ) means vars ## ------------------------------------------------------------------------ # CI for E(W1). means[1] + c(-1, 1) * qnorm(0.975) * sqrt(vars[1]) / sqrt(100) ## ------------------------------------------------------------------------ qbinom(c(0.025, 0.975), 11, 0.5) ## ------------------------------------------------------------------------ pbinom(8, 11, 0.5) - pbinom(1, 11, 0.5) ## ------------------------------------------------------------------------ f <- function() { X <- runif(11) Y <- sort(X) c(Y[2], Y[9]) } f() # try it out ## ----fig.height=3.5, fig.width=6----------------------------------------- nsimulations <- 100 C <- t(replicate(nsimulations, f())) matplot(C, type = "l", xlab = "Simulated sample", ylab = "CI") abline(c(0.5, 0), lty = 2, col = "darkgrey") mean((C[, 1] < 0.5) & (0.5 < C[, 2])) ## ------------------------------------------------------------------------ x <- rcauchy(25, location = 5) x ## ------------------------------------------------------------------------ x.bar <- mean(x) x.bar x.bar.tr <- mean(x, trim = 0.35) # exclude 35% of observations from each tail x.bar.tr ## ------------------------------------------------------------------------ B <- 1000 x.bar.boot <- numeric(B) x.bar.tr.boot <- numeric(B) for (i in 1:B) { x.ast <- sample(x, size = 25, replace = TRUE) x.bar.boot[i] <- mean(x.ast) x.bar.tr.boot[i] <- mean(x.ast, trim = 0.35) } ## ----fig.width=6, fig.height=8.2----------------------------------------- xlim <- range(x.bar.boot, x.bar.tr.boot) ylim <- c(0, 0.7) par(mfrow = c(2, 1), mar = c(5.1, 4.1, 1, 1)) hist(x.bar.boot, xlab = expression(bar(X)), freq = FALSE, xlim = xlim, ylim = ylim, col = "lightblue", main = NULL) hist(x.bar.tr.boot, xlab = expression(bar(X)[tr]), freq = FALSE, xlim = xlim, ylim = ylim, col = "lightblue", main = NULL) ## ------------------------------------------------------------------------ quantile(x.bar.tr.boot, c(0.025, 0.975)) ## ----fig.width=6, fig.height=4------------------------------------------- x <- faithful$waiting mean(x) hist(x, col = "lightblue") ## ----fig.width=6, fig.height=5------------------------------------------- B <- 10000 x.bar.boot <- numeric(B) for (i in 1:B) { x.ast <- sample(x, replace = TRUE) x.bar.boot[i] <- mean(x.ast) } hist(x.bar.boot, xlab = expression(bar(X)), freq = FALSE, col = "lightblue", main = NULL) ## ------------------------------------------------------------------------ quantile(x.bar.boot, c(0.025, 0.975))