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Probability: Difference between revisions
→Central Limit Theorem
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===Chebyshev's Inequality=== | ===Chebyshev's Inequality=== | ||
===Central Limit Theorem=== | ===Central Limit Theorem=== | ||
Very very important. Never forget this. | |||
For any distribution, the sample mean converges in distribution to normal. | |||
Let <math>\mu = E(x)</math> and <math>\sigma^2 = Var(x)</math><br> | |||
Different ways of saying the same thing: | |||
* <math>\sqrt{n}(\bar{x} - \mu) \sim N(0, \sigma^2)</math> | |||
* <math>\frac{\sqrt{n}}{\sigma}(\bar{x} - \mu) \sim N(0, 1)</math> | |||
* <math>\bar{x} \sim N(\mu, \sigma^2/n)</math> | |||
===Law of Large Numbers=== | ===Law of Large Numbers=== | ||