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Math Help - Unusual random variable density function

  1. #1
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    Unusual random variable density function

    A random variable X has the density function a*sin(x) + b*cos(x), if 0 < x < pi/2

    Find 'a' and 'b'
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  2. #2
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    Sorry, I forgot to include a piece of information relevant to the problem: E(X) = 1/3 + pi/6
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  3. #3
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    Quote Originally Posted by DannyOcean View Post
    A random variable X has the density function a*sin(x) + b*cos(x), if 0 < x < pi/2

    Find 'a' and 'b'
    Surely you would try get two equation in a and b from:

    \int_0^{\pi/2} f(x) \, dx = 1 and E(X) = \int_0^{\pi/2} x f(x) \, dx

    and then solve them simultaneously.
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