- #1
Chris L T521
Gold Member
MHB
- 915
- 0
Here's this week's problem!
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Problem: Let $X$ be a Poisson random variable with parameter $\lambda$, and let $Y$ be a Geometric random variable with parameter $p$ which is independent of $X$. In simplest terms of $\lambda$ and $p$, what is the value of $\Bbb{P}(Y>X)$?
Recall: The Poisson pmf is given by $f(x) = \dfrac{e^{-\lambda}\lambda^x}{x!}$ (with support $x\geq0$) and the Geometric pmf is given by $f(x) = p(1-p)^{x-1}$ (with support $x\geq 1$).
-----Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Problem: Let $X$ be a Poisson random variable with parameter $\lambda$, and let $Y$ be a Geometric random variable with parameter $p$ which is independent of $X$. In simplest terms of $\lambda$ and $p$, what is the value of $\Bbb{P}(Y>X)$?
Recall: The Poisson pmf is given by $f(x) = \dfrac{e^{-\lambda}\lambda^x}{x!}$ (with support $x\geq0$) and the Geometric pmf is given by $f(x) = p(1-p)^{x-1}$ (with support $x\geq 1$).
-----Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!