# Thread: Probability Density Function for the Lives of Light Bulbs

1. ## Probability Density Function for the Lives of Light Bulbs

I have been trying to solve a problem about the probability that 3 lightbulbs will last for 1500 hours of operation if the probability density function of a lightbulb is f(x) = 6[.25-(x-1.5)^2] when 1 <= x <= 2 and f(x) = 0 otherwise. x is measured in multiples of 1,000 hours. I tried doing [the integral from 1 to 1.5 of f(x)] CUBED, but I got an answer greater than 1. Does anyone know what I am doing wrong?

2. Looks like your integration is wrong. Try integrating again.

3. Originally Posted by oglemetender
I have been trying to solve a problem about the probability that 3 lightbulbs will last for 1500 hours of operation if the probability density function of a lightbulb is f(x) = 6[.25-(x-1.5)^2] when 1 <= x <= 2 and f(x) = 0 otherwise. x is measured in multiples of 1,000 hours. I tried doing [the integral from 1 to 1.5 of f(x)] CUBED, but I got an answer greater than 1. Does anyone know what I am doing wrong?
First you need to find $p = \int_{1.5}^2 f(x) \, dx$.

Then define the random variable Y = 'number of bulbs lasting more than 1500 hours'.

Y ~ Binomial(p, n = 3).

The required answer will obviously be p^3.