# Double Integral Probability

1. Jan 28, 2009

### CaptainEvil

1. The problem statement, all variables and given/known data

a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can modelthe probability of failure of these bulbs by an exponential density function $$\mu$$ = 1000, find the probability that both of the lamps bulbs will fail within 100 hours.

b) Another lamp has just one bulb of the same type as in part (a). if one bulb burns out and is replaced by a bulb of the same time, find the probability that the two bulbs fail within a total of 1000 hours.

2. Relevant equations

3. The attempt at a solution

I'm pretty sure $$\mu$$ = double integral on a region D of xf(x,y)dA but I don't know what my region or f(x,y) would be.

2. Jan 28, 2009

### NoMoreExams

1) Think about the support for exponential.
2) Why do you think it's x*f(x,y)?

3. Jan 28, 2009

### CaptainEvil

formula's from my textbook give

$$\mu$$1 = double integral over the region of x*f(x,y)
and same for $$\mu$$2 with y*f(x,y)

It's the same as solving for mass and centre of mass over a region with double integrals

4. Jan 28, 2009

### NoMoreExams

Well you want P(bulb1 fails and bulb2 fails) they are independent, so can you rewrite that?