On this set of exercises, we are going to explore some of the probability functions in R with practical applications. Basic probability knowledge is required.

Note: We are going to use random number functions and random process 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 numbers). For this set of exercises we will use set.seed(1), don’t forget to specify it before every random exercise.

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 random numbers.  Set your seed to 1 and generate 10 random numbers using runif and save it in an object called random_numbers.

Exercise 2

Using the function ifelse and the object random_numbers simulate coin tosses. Hint: If random_numbers is bigger than .5 then the result is head, otherwise is tail.

Another way of generating random coin tosses is by using the rbinom function. Set the seed again to 1 and simulate with this function 10 coin tosses. Note: The value you will obtain is the total number of heads of those 10 coin tosses.

Exercise 3

Using the function rbinom to generate 10 unfair coin tosses with probability success of 0.3. Set the seed to 1.

Exercise 4

We can simulate rolling a die in R with runif. Save in an object called die_roll 1 random number with min = 1 and max = 6. This mean that we will generate a random number between 1 and 6.

Apply the function ceiling to die_roll. Don’t forget to set the seed to 1 before calling runif.

Exercise 5

Simulate normal distribution values. Imagine a population in which the average height is 1.70 m with an 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 applying the function summaryto it.

Exercise 6

a) What’s the probability that a person will be smaller than 1.90? Use pnorm
b) What’s the probability that a person will be taller than 1.60? Use pnorm

Exercise 7

The waiting time (in minutes) at a doctor’s clinic follows an exponential distribution with a rate parameter of 1/50. Use the function rexp to simulate the waiting time of 30 people at the doctor’s office.

Exercise 8

What’s the probability that a person will wait less than 10 minutes? Use pexp

Exercise 9

What’s the waiting time average?

Exercise 10

Let’s assume that patients with a waiting time bigger than 60 minutes leave. Out of 30 patients that arrive to the clinic how many are expected to leave? Use qexp