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    i can usually do these type of questions but this one has baffled me.

    the random variable x has probability density function f(x)=(3x^k, 0<x<1)
    Where k is a positive integer, find the value of k.
    I just cant seem to get the correct answer
    i have intergrated it and equalled it to 1 and then tried to rearrange it but i dont get the correct answer. Can someone show me some steps to do it
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    integrating 3x^k

    gives \frac{3x^{k+1}}{k+1}

    if you set the limit between 1 and 0 and make it equal to 1 then

     \frac{3*1^{k+1}}{k+1}+ \frac{3*0^{k+1}}{k+1}=1

    1 to any real number is 1. 0 to any real number (except 0) is 0. therefore:

    \frac{3}{k+1}=1

    and you can solve that.
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    Can you show your working? Either you have a silly error somewhere for which you will kick yourself, or the book is wrong.
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Updated: January 13, 2010

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