Publications by aardvarkfunnyxia
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When a certain driver parks their car in the evenings, they are equally likely to remember or to forget to switch off the headlights. Giving your answers in their simplest index form, find the probability that on the next 16 occasions that they park their car in the evening, they forget to switch off the headlights: a) 14 more times than they rem...
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set.seed(12345) Generate 4 sets of 100 points from the N(0, 1) distribution random_normal_1 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_2 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_3 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_4 <- rnorm ( n = 100, mean = 0, sd = 1 ) compare each of the sets using histogram par (mfrow ...
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Exercise 8.1. x_values = seq ( -3, 3, length.out = 100000) plot ( x_values, dnorm (x_values, mean = 0, sd = 1), type = "l") abline ( v = c (-3, 3), col = "red", lty = 2, lwd = 2) total_area <- pnorm (Inf, mean = 0, sd = 1) area_below_3 <- pnorm (3, mean = 0, sd = 1) area_between <- ((2 * area_below_3 - 1) / total_area ) *100 print...
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Exercise 8.4 – an optional one set.seed(12345) Generate 4 sets of 100 points from the N(0, 1) distribution random_normal_1 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_2 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_3 <- rnorm ( n = 100, mean = 0, sd = 1 ) random_normal_4 <- rnorm ( n = 100, mean = 0, sd = 1 ) compare each of the...
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Using sample() in R allows you to take a random sample of elements from a dataset or a vector,either with or without replacement The basic syntax is the following sample (x, size, replace = FALSE, prob = NULL) (see ?sample) Generating a sample from a Vector Suppose we have a vector with 10 elements vector <- c (seq (1:10)) # to generate a random ...
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poi5 <- dpois(0:20, lambda = 5) plot (poi5, pch = 20, xlab = "value of x", ylab = "probability", main = "Lines of mean = 5", ylim = c(0,0.25)) lines(poi5, lwd = 2) ## the mean of the distribution Poi(5) mean_poi5 <- sum (0:20 * poi5) mean_poi5 ## [1] 4.999998 ## add the following lines (3): ### bin(10,0.5) distribution in red bin10_0....
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Exercise 7.1. ############################################### ### Expectation: (Note: in all of the following questions, p = 0.2, days = 365) days <- 365 p <- 0.2 E <- p * days print(E) ## [1] 73 ### Probability that I wear an ironed shirt 16 days or fewer: sum (dbinom (x = 1:16, size = days, prob = p)) ## [1] 4.096763e-18 Exercise 7.2. ###########...
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Exercise 7.1. ############################################### ### Expectation: (Note: in all of the following questions, p = 0.2, days = 365) days <- 365 p <- 0.2 E <- p * days print(E) ## [1] 73 ### Probability that I wear an ironed shirt 16 days or fewer: sum (dbinom (x = 1:16, size = days, prob = p)) ## [1] 4.096763e-18 Exercise 7.2. ###########...
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## Given that we have a normal distribution X ~ N (2, 4) show that P (X < 4) = 0.8413447 pnorm (4, mean= 2, sd = sqrt(4)) ## [1] 0.8413447 What are qX1 such that P(X < qX1) = 0.95 and qX2 such that P(X < qX2) = 0.975? qx1 <- qnorm (0.95, mean = 2, sd = sqrt(4)) qx1 ## [1] 5.289707 qx2 <- qnorm (0.975, mean = 2, sd = sqrt (4)) qx2 ## [1] 5.919928 Dr...
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Exercise 7.11. Create a QQ plot for the Handspan data with an appropriate heading. Do you think that the data appear normal? Why? qanda <- read.csv("selective_affinities.csv") qanda_modified <- read.csv("selective_affinities_aftermodified.csv") attach (qanda_modified) qqnorm (y = Handspan, pch = 20) qqline (Handspan, col = "red", lwd = 2) detach(...
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