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Math Help - Probability Density Function for the Lives of Light Bulbs

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    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?
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    MHF Contributor harish21's Avatar
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    Looks like your integration is wrong. Try integrating again.
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    Quote Originally Posted by oglemetender View Post
    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.
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