In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.

It’s the probability that a normal random variable with mean 0 and variance 0.5 take value between [-x, x]. It is denoted by erf(x) and calculated by:-

In **cmath** library of C++, error function has been already implemented. There are two such functions:-

**erf(x)**: This inbuilt function calculate the error function for input value of x. Parameter x which can be int or float or double. It return a double which is erf(x).-
**erfc(x)**: This inbuilt function calculate the complementary of error function for input value of x. Parameter x which can be int or float or double. It return a double which is 1 – erf(x).

`/* C++ code to use erf */` `#include <iostream> ` `#include <cmath> /* erf */ ` ` ` `using` `namespace` `std; ` ` ` `double` `findProbability(` `double` `a) ` `{ ` ` ` `double` `prob_x_a = erf(a); ` ` ` `return` `prob_x_a; ` `} ` ` ` `int` `main () ` `{ ` ` ` `double` `a = 0.25; ` ` ` `cout << ` `"probability that normal r.v "` ` ` `"X takes value between "` ` ` `<< -a << ` `" & "` `<< a << ` `" is "` ` ` `<< findProbability(a) << endl; ` ` ` `return` `0; ` `} ` |

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Output:

probability that normal r.v X takes value between -0.25 & 0.25 is 0.276326

Reference :

Wikipedia

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