What Is the Joint PDF for Durations of Bulbs with Exponential Distribution?

[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?

 

[statdad]

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

 

[Gp7417]

Yes the durations can be indipendent.

 

[statdad]

What do you know about distributions of independent random variables?

 

[Gp7417]

Is this the right answer?
$$f(t_1,t_2...t_n)=\lambda^n e^{-\lambda \sum_{i=1}^{n}t_i}$$