# Geometric Distribution problem

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

• 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 $n\geqslant0$.