# Solving PDF with set boundary values

1. Oct 13, 2012

### Ein Krieger

I am give probability distribution function f(x)=(e(-x/1000))/1000 of the time to failure of an electronic component in a copier

The question is to determine the number of hours at which 10% of all components have failed.

My solution:
1) PDF was integrated to obtain: f(x)= e(-x/1000)

2) Then, I used e(-x/1000)=0.1 with upper boundary x, and lower boundary is 0 to find x as the number of hours at which all 10% of components have failed. However, entering it in calculator, I couldn't obtain solution. What did I wrong here?

2. Oct 13, 2012

### Stephen Tashi

You're using "f(x)" inconsistently to stand for two different things and your antiderivative is missing a negative sign.

$\int \frac{e^{-x/1000}}{1000} dx = - e^{-x/1000} + C$

You can't compute a deterministic answer for the time when 10% of the components have failed since that time is a random variable. Perhaps you want to compute the time at which the probability that a component has failed then or earlier reaches .10. Your description of what you did with the calculator isn't clear.

3. Oct 14, 2012

### awkward

Ein Krieger,

I am pretty sure you are leaving out one critical part of the definition of f(x). The pdf is

$$f(x) =\frac{1}{1000} e^{-x / 1000}$$
for $x \ge 0$, zero otherwise.

So you should integrate f(x) from 0 to x; you will get a different answer for the cdf than you got before.

4. Oct 14, 2012

### Ein Krieger

Yes. Sure. You are right. Time is continuous variable so it is inconsistent to try to define exact probability. All we need is to get probability for time range.

I have already calculated, and I got 105 hours. is it right?