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Math Help - Probability Distribution Functions

  1. #1
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    Probability Distribution Functions

    Hello Friends

    I need help with a past exam paper question for statistics; it's from a first-year undergraduate paper. It goes like this:

    The probability distribution of a random variable has the following density function:

    (x) = cx^2(x-1) if 0=<x=<1
    = o otherwise

    and we are given a probability graph with a normal distribution with f(x) on the y-axis. x: 0=<x=<1 and f(x): 0=<x=<1 .

    i) Show that c=30.

    Can anyone please advise how I would go about solving this? I don't want the question solved for me, just a couple of hints.

    Hope this is okay. Muchos gracios.

    Best,

    ThetaPhi
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  2. #2
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    solve this

    \displaystyle \int_0^1 cx^2(x-1) ~dx = 1
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  3. #3
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    Quote Originally Posted by pickslides View Post
    solve this

    \displaystyle \int_0^1 cx^2(x-1) ~dx = 1
    Yep, done that. I moved c in front of the integral and then solved to find that the integral is 1/12. Hence, as per the integral in your quote, c=12. But this is my point, why c=30?

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  4. #4
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    Quote Originally Posted by ThetaPhi View Post
    Yep, done that. I moved c in front of the integral and then solved to find that the integral is 1/12. Hence, as per the integral in your quote, c=12. But this is my point, why c=30?

    Whoever said c = 30 is obviously wrong and you will need to discuss it with them. By the way, c = 12 is wrong too.
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