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Home work assignment i'm struggling with , i've been on this for an hour and have nothing :

Let $X_1, \ldots X_n$ be a group of independent variables with geometric distribution: $X_i \sim \operatorname{Geom}(p_i)$. Let $Y = \min \{X_1 , \ldots , X_n\}$.

How is $Y$ distributed?

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Can you handle from here? en.wikipedia.org/wiki/… –  Alex Dec 2 '12 at 10:55
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1 Answer

up vote 2 down vote accepted

Hints:

  • A random variable $X$ is geometric with parameter $p$ if and only if $\mathbb P(X\geqslant k)=$$_______$ for every $k\geqslant0$.
  • The random variable $Y=\min\{X_1,\ldots,X_n\}$ is such that $[Y\geqslant k]=\bigcap\limits_{i=1}^n[X_i\geqslant k]$ and the random variables $(X_i)_i$ are independent hence $\mathbb P(Y\geqslant k)=\displaystyle\prod\limits_{i=1}^n$$______$ for every $n\geqslant0$.
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