Class Demo 9-2 11am

Coding Basic

create a vector

v <- c(1, 4, 9, 16, 25)

operations on vectors

Take square root of every element of a vector

sqrt(v)

## [1] 1 2 3 4 5

v + 1

## [1]  2  5 10 17 26

A function applied to a vector applies the function to each element.

to update vector v (assign as the same name)

v <- sqrt(v)

to undo, run the original function again:

v <- c(1, 4, 9, 16, 25)

Usually good practice to give new names to new things:

w <- sqrt(v)

Which elements of v are bigger than 10?

v > 10

## [1] FALSE FALSE FALSE  TRUE  TRUE

Other operations: greater than or equal to >= Less than < Less than or equal to <= Equals == (two equal signs) Not equals !=

Create new vector of elements of logicals for if elements of v are > 10.

u <- v > 10

How many elements are greater than 10?

2, just by counting

Ask R:

sum(u)

## [1] 2

How do we write functions in R?

structure

name_of_function <- function(variable1, variable6, pizza){
  variable1 + variable6*pizza
}

Recall the birthday problem. Suppose we have a group of k people and each chooses a number between 1 and n.

The probability of a match is

1 - n!/((n-k)!*n^k)

\[ 1 - \frac{n!}{(n-k)! n^k} = 1 - \binom{n}{k}\frac{k!}{n^k} \]

Write function to input n,k and return probability

prob_bday_match <- function(n_bdays, k_people){
  1 - choose(n_bdays, k_people)*factorial(k_people)/(n_bdays^k_people)
}

How to plot in R (basic)?

To plot function of 1 variable:

Goal: Plot birthday probability for 25 students choosing from numbers between 50 and 25000.

View function at equally spaced points in domain

n_bdays <- seq(from = 50, to = 1000, by = 25)

Evaluate function on n_bdays

probs <- prob_bday_match(n_bdays, 25)

Use plot function applied to vectors of inputs and outputs

plot(n_bdays, probs)