# cdfHyperGeo¶

## Purpose¶

Computes the cumulative distribution function for the hypergeometric distribution.

## Format¶

p = cdfHyperGeo(x, pop_size, n_marked, n_items)
Parameters:
• x (NxK matrix, Nx1 vector or scalar) – must be a positive number and $$0 < x < pop\_size$$

• pop_size (matrix) – The size of the population from which draws will be made. ExE conformable with x. $$pop\_size > x,\:\ n\_marked\:\ and\:\ n\_items$$.

• n_marked (matrix) – The number of marked items. ExE conformable with x. $$0 < n\_marked$$.

• n_drawn (matrix) – The number of items drawn from the population. ExE conformable with x. $$0 < n\_drawn < pop\_size$$.

Returns:

p (NxK matrix, Nx1 vector or scalar) – The probability of drawing x or fewer marked items.

## Examples¶

You are given 120 hard drives, 14 of which are known to be bad. What is the probability of drawing 2 or fewer bad hard drive if you randomly select 12 drives?

// Value of interest
x = 2;

// Total population
pop_size = 120;

// Marked items
n_marked = 14;

// Number drawn
n_drawn = 12;

// Call cdfHyperGeo
p = cdfHyperGeo(x, pop_size, n_marked, n_drawn);


After running the code above, p is equal to:

0.85284036


Continuing with the example above, what are the probabilities of drawing 4 or fewer bad hard drives if you draw 20 or 40 hard drives?

// Value of interest
x = 4;

// Total population
pop_size = 120;

// Marked items
n_marked = 14;

// Number drawn
n_drawn = { 20, 40 };

p = cdfHyperGeo(x, pop_size, n_marked, n_drawn);
print p;


After running the code above, p is equal to:

0.94307042
0.47070798


## Remarks¶

For invalid inputs, cdfHyperGeo() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.