# Probability functions beginner

**R-exercises**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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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 `summary`

to 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`

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