# Thread: Continuous random variables and their probability distributions question

1. ## Continuous random variables and their probability distributions question

A probability density function for the lifetime t hours of Electra light globes is given by the rule:
f(t)=ke^(-t/200), t > 0
Find:
a) the value of the constant k
b) the probability that a bulb will last more than 1000 hours.
I understand how to complete part b of the question, however I need to answer a beforehand, and I have no idea even where to begin to find the answer.
Thanks.

2. ## Re: Continuous random variables and their probability distributions question

Originally Posted by juliacoolness
A probability density function for the lifetime t hours of Electra light globes is given by the rule:
f(t)=ke^(-t/200), t > 0
Find:
a) the value of the constant k
b) the probability that a bulb will last more than 1000 hours.
I understand how to complete part b of the question, however I need to answer a beforehand, and I have no idea even where to begin to find the answer.
Thanks.
To be a density you need:

$\displaystyle \int_0^{\infty}ke^{-t/200}\; dt =1$

This will determine the value of $\displaystyle k$

CB

3. ## Re: Continuous random variables and their probability distributions question

Thank you so much. I used that and I got the right answer of k=1/200.