# Exam P Practice Problem 16 – Conditional Probability and Exponential Distribution

_________________________________________________________

Practice Problem 16A
Losses $X$ and $Y$ due to two different perils are independently and identically distributed according to the density function $f(x)=0.25 \ e^{-0.25 \ x}$ where $x>0$. If the total loss for the two perils is greater than $2$, what is the probability that $X$ is greater than $1$?

Practice Problem 16B
Losses $X$ and $Y$ due to two different perils are independently and identically distributed according to the density function $f(x)=0.125 \ e^{-0.125 \ x}$ where $x>0$. If the total loss for the two perils is greater than $6$, what is the probability that $X$ is less than $4$?

_________________________________________________________

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

_________________________________________________________

_________________________________________________________

$\copyright \ 2013$

### One response

1. Hi Dan, Did you explain similar problems in your website?
I don’t have any clue to calculate the required conditional probability after finding the pdf of total loss.
Any help is appreciated.

Thank you.