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.

Re: Continuous random variables and their probability distributions question

Quote:

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

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.