Distributacalcul (version 0.2.2)

E_hyper: Expected value of the Hypergeometric distribution

Description

Expected value 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

E_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: V_hyper()

Examples

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

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

# }