Documentation

# `stats`::`normalPDF`

Probability density function of the normal distribution

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## Syntax

```stats::normalPDF(`m`, `v`)
```

## Description

`stats::normalPDF(m, v)` returns a procedure representing the probability density function of the normal distribution with mean `m` and variance `v`.

The procedure `f := stats::normalPDF(m, v)` can be called in the form `f(x)` with an arithmetical expression `x`. The value `exp(-(x - m)^2/(2*v))/sqrt(2*PI*v)` is returned.

If `x` is a floating-point number and both `m` and `v` can be converted to floating-point numbers, this value is returned as a floating-point number. Otherwise, a symbolic expression is returned.

Numerical values for m and v are only accepted if they are real and v is positive.

## Environment Interactions

The function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

We compute the probability density with mean m = 2 and variance v = 4 at various points:

```f := stats::normalPDF(2, 4): f(-infinity), f(-3), f(2.0), f(PI), f(infinity)```
` `
`delete f:`

### Example 2

We use symbolic arguments:

`f := stats::normalPDF(m, v): f(x), f(0.4)`
` `

When numerical values are assigned to m and v, the function f starts to produce numerical values:

`m := PI: v := 2: f(3), f(3.0)`
` `
`delete f, m, v:`

## Parameters

 `m` The mean: an arithmetical expression representing a real value `v` The variance: an arithmetical expression representing a positive real value