(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes component 2 to fail, and a type 3 shock causes both components 1 and 2 to fail. The times until shocks 1, 2, and 3 occur are independent exponential random variables with respective rates [itex]\lambda_1, \lambda_2, \lambda_3[/itex]. Let [itex]X_i[/itex] denote the time at which component i fails, i = 1, 2. The random variables [itex]X_1, X_2[/itex] are said to have a joint bivariate exponential distribution. Find [itex]P\{X_1 > s, X_2 > t\}[/itex].

The attempt at a solution

This problem would by so much easier if type 3 shocks didn't exists as it would make [itex]X_1, X_2[/itex] independent. Anywho...

Let [itex]Y_1, Y_2, Y_3[/itex] be the times shocks of type 1, 2, 3 occurred. I know I'm going to have to deal with the joint distribution of these three random variables. However, I can't think of anything. I need a little hint.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Joint Bivariate Exponential Distribution

**Physics Forums | Science Articles, Homework Help, Discussion**