Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
    
Can you handle from here? en.wikipedia.org/wiki/… – Alex Dec 2 '12 at 10:55
up vote 3 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 $n\geqslant0$.
share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.