# Determination of a Join pdf

1. Dec 19, 2009

### Gp7417

Determination of a Joint pdf

Hi all! Someone can help me with this problem?

The duration of a certain type of bulbs has a exponential distribution with known parameter $$\lambda$$. Consider a set of n bulbs. Which is the joint pdf of the durations $$t_{i}$$ of the $$n$$ bulbs?

Last edited: Dec 20, 2009
2. Dec 20, 2009

Can you assume that the durations' distributions are independent? If so, there shouldn't be a problem.

3. Dec 20, 2009

### Gp7417

Yes the durations can be indipendent.

4. Dec 20, 2009

$$f(t_1,t_2...t_n)=\lambda^n e^{-\lambda \sum_{i=1}^{n}t_i}$$