Let be a continuous random variable with probability density function . If exists, then

For the expected value we have

The probability density function of a continuous random variable is continuous.

For a continuous random variable for any one has .

If , , …, is a partition of the sample space, then for any event

If , then is the impossible event.

If are events, then occurs if occurs and does not occur.

The integral of a vector field on the parametrized surface is:

If is a potential function of the vector field , the starting point of a curve is and the ending point is , then

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