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Probability: Difference between revisions
→Gamma Distributions
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===Gamma Distributions=== | ===Gamma Distributions=== | ||
Note exponential distributions are also Gamma distrubitions | Note exponential distributions are also Gamma distrubitions | ||
If <math>X \sim \Gamma(k, \theta)</math> then <math>\lambda X \sim \Gamma(k, c\theta)</math>.<br> | |||
If <math>X_1 \sim \Gamma(k_1, \theta)</math> and <math>X_2 \sim \Gamma(k_2, \theta)</math> then <math>X_2 + X_2 \sim \Gamma(k_1 + k_2, \theta)</math>. | |||
===Gamma and Beta=== | ===Gamma and Beta=== | ||
If <math>X_1 \sim \Gamma(\alpha, \theta)</math> and <math>X_2 \sim \Gamma(\beta, \theta)</math>, then <math>\frac{X_1}{X_1 + X_2} \sim B(\alpha, \beta)</math> | If <math>X_1 \sim \Gamma(\alpha, \theta)</math> and <math>X_2 \sim \Gamma(\beta, \theta)</math>, then <math>\frac{X_1}{X_1 + X_2} \sim B(\alpha, \beta)</math> | ||