Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 18 / b / ii

Table of contents
- Solution ii

Solution

When the relevant moments are finite, the mean and variance are

μ = E [X] = \int_{- \infty}^{\infty} x f (x) d x, σ^{2} = E [(X - μ)^{2}] = \int_{- \infty}^{\infty} (x - μ)^{2} f (x) d x .

Equivalently,

σ^{2} = \int x^{2} f (x) d x - μ^{2}

. The mean requires an integrable absolute first moment; finite second moment guarantees both quantities are finite.

 Ancestors (13)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version