# Probability functions intermediate

August 31, 2017
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In this set of exercises, we are going to explore some of the probability functions in R by using practical applications. Basic probability knowledge is required. In case you are not familiarized with the function apply, check the R documentation.

Note: We are going to use random numbers functions and random processes functions in R such as runif. A problem with these functions is that every time you run them, you will obtain a different value. To make your results reproducible you can specify the value of the seed using set.seed(‘any number’) before calling a random function. (If you are not familiar with seeds, think of them as the tracking number of your random number process.) For this set of exercises, we will use set.seed(1).Don’t forget to specify it before every exercise that includes random numbers.

Answers to the exercises are available here. If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.

Exercise 1

Generating dice rolls Set your seed to 1 and generate 30 random numbers using runif. Save it in an object called random_numbers. Then use the ceiling function to round the values. These values represent rolling dice values.

Exercise 2

Simulate one dice roll using the function rmultinom. Make sure n = 1 is inside the function, and save it in an object called die_result. The matrix die_result is a collection of 1 one and 5 zeros, with the one indicating which value was obtained during the process. Use the function whichto create an output that shows only the value obtained after the dice is rolled.

Exercise 3

Using rmultinom, simulate 30 dice rolls. Save it in a variable called dice_result and use apply to transform the matrix into a vector with the result of each dice.

Exercise 4

Some gambling games use 2 dice, and after being rolled they sum their value. Simulate throwing 2 dice 30 times and record the sum of the values of each pair. Use rmultinomto simulate throwing 2 dice 30 times. Use the function apply to record the sum of the values of each experiment.

Learn more about probability functions in the online course Statistics with R – Advanced Level. In this course you will learn how to

• work with different binomial and logistic regression techniques,
• know how to compare regression models and choose the right fit,
• and much more.

Exercise 5

Simulate normal distribution values. Imagine a population in which the average height is 1.70 m with a standard deviation of 0.1. Using rnorm, simulate the height of 100 people and save it in an object called heights.

To get an idea of the values of heights, use the function summary.

Exercise 6

90% of the population is smaller than ____________?

Exercise 7

Which percentage of the population is bigger than 1.60 m?

Exercise 8

Run the following line code before this exercise. This will load a library required for the exercise.

if (!'MASS' %in% installed.packages()) install.packages('MASS')
library(MASS)

Simulate 1000 people with height and weight using the function mvrnorm with mu = c(1.70, 60) and
Sigma = matrix(c(.1,3.1,3.1,100), nrow = 2)

Exercise 9

How many people from the simulated population are taller than 1.70 m and heavier than 60 kg?

Exercise 10

How many people from the simulated population are taller than 1.75 m and lighter than 60 kg?

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