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Probability: Difference between revisions
→Chi-Sq Distribution
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===Chi-Sq Distribution=== | ===Chi-Sq Distribution=== | ||
* The ratio of two normalized Chi-sq is an F-distributions | * The ratio of two normalized Chi-sq is an F-distributions | ||
** If <math>X \sim \chi^2_{d1}</math> and <math>Y \sim \chi^2_{d2}</math> then <math>\frac{X/d1}{Y/d2} \sim F(d1,d2)</math> | |||
* If <math>Z_1,...,Z_k \sim N(0,1)</math> then <math>Z_1^2 + ... + Z_k^2 \sim \Chi^2(k)</math> | * If <math>Z_1,...,Z_k \sim N(0,1)</math> then <math>Z_1^2 + ... + Z_k^2 \sim \Chi^2(k)</math> | ||
* If <math>X_i \sim \Chi^2(k_i)</math> then <math>X_1 + ... + X_n \sim \Chi^2(k_1 +...+ k_n)</math> | * If <math>X_i \sim \Chi^2(k_i)</math> then <math>X_1 + ... + X_n \sim \Chi^2(k_1 +...+ k_n)</math> | ||