If is a random variable and is its cumulative distribution function, then .

The probability density function is a moronically increasing function.

For conditional probability .

If and are events, then .

Two events are independent if .

The integral of a vector field on the parametrized surface

If a vector field is conservative, then for any curves the line integral is zero.

If is a critical point of the function and the principal minors of the Hessian are and , then has a minimum at .

The directional derivative of at with respect to the unit vector is

The function is differentiable at if there exists a linear map such that