The variance can be written as Var[X]=E[X^2]-(E[X])^2. Use this form to prove that the Var[X] is always non-negative, i.e., show that E[X^2]>=(E[X])^2.(adsbygoogle = window.adsbygoogle || []).push({});

Use Jensen's Inequality.

Any sugestions? I just tried to prove that a function g(t) is continuous and twice differentiable, such that g''(t) > 0 which must imply it is convex.

Then, I am stuck with the proof.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Jensen's Inequality

Loading...

Similar Threads - Jensen's Inequality | Date |
---|---|

Bell's theorem in nLab | Oct 26, 2015 |

Exponential Inequalities | Apr 28, 2013 |

The var(x+y) Inequality Proof | Apr 8, 2013 |

Jensen inequality, unexplained distribution, very confusing problem | Jan 29, 2012 |

Jensen's Inequality | Mar 4, 2010 |

**Physics Forums - The Fusion of Science and Community**