Vectors

To create a vector, use the c command, which stands for concatenate or combine.

> v <- c(3,1,4,1,5,9)

To create a scalar:

> n <- 100

R views n as a vector of length 1.

You can inspect many vector properties immediately:

> sum(v)
[1] 23
> max(v)
[1] 9
> min(v)
[1] 1
> length(v)
[1] 6

Subvectors are also easy:

> v[c(1,3,5)]
[1] 3 4 5
> v[-(2:4)]
[1] 3 5 9

In R, indexing starts from 1 instead of 0.

Shortcut for (1,2,...,n):

v2 = 1:28

Operations are componentwise. For example:

1/(1:20)^5

If a shorter vector is added to a longer one, the shorter one is recycled:

> v <- c(3,1,4,1,5,9)
> v3 <- c(100, 200)
> v + v3
[1] 103 201 104 201 105 209

Factorials and Binomial Coefficients

Use factorial(n) for $n!$ and choose(n,k) for $\binom{n}{k}$.

For logarithms, use lfactorial(n) and lchoose(n,k).

Sampling and Simulation

The sample command generates random samples in R.

> n <- 10; k <- 5
> sample(n,k)

Sampling with replacement and probabilities:

> sample(4, 10, replace = TRUE, prob = c(0.1, 0.2, 0.3, 0.4))
 [1] 3 4 4 4 3 2 4 3 3 2

The replicate command is useful for Monte Carlo simulation.

Problem (matching problem) Consider a shuffled deck of n cards labeled 1 through n. You flip them one by one while saying 1 through n aloud. You win if the spoken number matches the card being turned over at any point. What is the probability of winning?

贡献者: Junyuan He