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Math Help - Probability distribution derivation

  1. #1
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    Probability distribution derivation

    This is the probability distribution:

    p(x) = ax^n , 0<= x <=1

    Derive an expression for the constant a, to normalize p(x).

    Whats a good starting point for this derivation? My initial thought was to take p(x) = dy/dx, separate variables and integrate using the bounds for x on the right side and then setting a equal to the answer. But I don't think this makes sense. Any suggestions? Thanks,

    Kim
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  2. #2
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    Quote Originally Posted by Kim Nu View Post
    This is the probability distribution:

    p(x) = ax^n , 0<= x <=1

    Derive an expression for the constant a, to normalize p(x).

    Whats a good starting point for this derivation? My initial thought was to take p(x) = dy/dx, separate variables and integrate using the bounds for x on the right side and then setting a equal to the answer. But I don't think this makes sense. Any suggestions? Thanks,

    Kim
    You need to understand what "normalize" means in this setting. It says that a is such that p is the density of a probability distribution. In other words, it must be such that \int_{\mathbb{R}} p(x)dx=1 (the total mass equals 1). Substitute the value of p(x) in this equation (note that p(x)=0 is x\notin[0,1]), compute the integral, and deduce a.
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  3. #3
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    Thanks!
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