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    Probability: Random Variable and Probability Density Function

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    Problem 1: A random variable X takes values between 0 and infinity with a probability density function
    f(x) = A + Be^(-x) for 0 <= x <= infinity.
    a) find A and B
    b) find expected value of X
    c) what is the median of X?

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    Solution Preview

    integration(0 to infinity)[f(x) dx] = 1 (total probability = 1)
    =>integration(0 to infinity)[(A+B*exp(-x)) dx] = 1
    => A*x - B*exp(-x)|(0 to infinity) = 1
    => A = 0 ( because x value is from 0 to infinity, because of ...

    Solution Summary

    The expected value and median of a random variable are found. The full calculations are shown.