# Probability Distribution Functions

• May 12th 2011, 02:12 PM
ThetaPhi
Probability Distribution Functions
Hello Friends (Bow)

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 (Cool)
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• May 12th 2011, 02:30 PM
pickslides
solve this

$\displaystyle \displaystyle \int_0^1 cx^2(x-1) ~dx = 1$
• May 12th 2011, 05:49 PM
ThetaPhi
Quote:

Originally Posted by pickslides
solve this

$\displaystyle \displaystyle \int_0^1 cx^2(x-1) ~dx = 1$

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?