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Probability: Difference between revisions
→Expectation and Variance
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* <math>\bar{X} \sim N(\mu, \sigma^2 / n)</math> | * <math>\bar{X} \sim N(\mu, \sigma^2 / n)</math> | ||
* <math>(n-1)S^2 / \sigma^2 \sim \chi^2(n-1)</math> | * <math>(n-1)S^2 / \sigma^2 \sim \chi^2(n-1)</math> | ||
===Jensen's Inequality=== | |||
{{main | Wikipedia: Jensen's inequality}} | |||
Let g be a convex function (i.e. second derivative is positive). | |||
Then <math>g(E(x)) \leq E(g(x))</math>. | |||
==Moments and Moment Generating Functions== | ==Moments and Moment Generating Functions== | ||