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Probability: Difference between revisions
→Exponential Distribution
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* If <math>\epsilon_1, ..., \epsilon_n</math> are exponential distributions then <math>\min\{\epsilon_i\} \sim \exp(\sum \lambda_i)</math> | * If <math>\epsilon_1, ..., \epsilon_n</math> are exponential distributions then <math>\min\{\epsilon_i\} \sim \exp(\sum \lambda_i)</math> | ||
* Note that the maximum is not exponentially distributed | * Note that the maximum is not exponentially distributed | ||
* However, if <math>X_1, ..., X_n \sim \exp(1)</math> then <math>Z_n=n\exp(\max\{\epsilon_i\}) \rightarrow \exp(1)</math> | ** However, if <math>X_1, ..., X_n \sim \exp(1)</math> then <math>Z_n=n\exp(\max\{\epsilon_i\}) \rightarrow \exp(1)</math> | ||
===Gamma Distribution=== | ===Gamma Distribution=== | ||