Distributacalcul (version 0.2.2)

V_hyper: Variance of the Hypergeometric distribution

Description

Variance of the Hypergeometric distribution where we have a sample of k balls from an urn containing N of which m are white and n are black.

Usage

V_hyper(N = n + m, m, n = N - m, k)

Arguments

N

Total number of balls (white and black) in the urn. $N=n+m$

m

Number of white balls in the urn.

n

Number of black balls in the urn. Can specify n instead of N.

k

Number of balls drawn from the urn, k = 0, 1, ..., m + n.

Value

Function :

• E_hyper gives the expected value.

• V_hyper gives the variance.

Invalid parameter values will return an error detailing which parameter is problematic.

Details

The Hypergeometric distribution for $N$ total items of which $m$ are of one type and $n$ of the other and from which $k$ items are picked has probability mass function : $$Pr(X=x)=\frac{\left(\frac{m}{k}\right)\left(\frac{n}{k-x}\right)}{\left(\frac{N}{k}\right)}$$ for $x=0,1,\dots ,min(k,m)$.

See Also

Other Hypergeometric Distribution: E_hyper()

Examples

# NOT RUN {
# With total balls specified
V_hyper(N = 5, m = 2, k = 2)

# With number of each colour of balls specified
V_hyper(m = 2, n = 3, k = 2)

# }