R (Language)

Combinations in R

The general formula for finding a combination in R is:

choose(n, k)

Go back to this example:

Ex: Stock Portfolio

Suppose there are 100 possible stocks

• You want to invest equally in five stocks (20% in each). How many possible portfolios are there? (Order doesn’t matter here)
• You want to form a 30%/25%/20%/15%/10% weighted portfolio of five stocks. How many possible portfolios are there? (Order does matter here)

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If finding the first bullet point, where order doesn’t matter:

choose(100, 5)

Permutations in R

No built in function for permutations, but its very simple, because the equation for permutations itself is simple.

Recall the Permutation general formula:

P_{n,k}=\frac{n!}{(n-k)!}

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We can express this in R as:

factorial(n)/factorial(n-k)

Normal Distribution in R

dnorm(x, mean, sd) can be used to find the PDF of a normal random variable given the standard deviation and mean. It defaults to the PDF for $XN(0,1)$

pnorm(x, mean, sd) can be used to find the PDF of a normal random variable given the standard deviation and mean, it defaults to the CDF for $XN(0,1)$