# n-th percentile

• June 7th 2010, 10:58 AM
losm1
n-th percentile
I need to find 10th percentile of random variable X with PDF defined with:

$
f(x) = \left\{\begin{array}{cc}c(x-x^3)&0< x < 1\\0&x\le 0 \vee x\ge 1 \end{array}\right.
$

where $c\in \mathbb{R}$ is const that should be found too.
By integrating f from 0 to $x$ I got cumulative dist. function $F(x) = c \frac{2x^2 - x^4}{4}$, so $c=4$.

First, is this approach OK, and second, how can I calculate required percentile?

Thanks guys
• June 7th 2010, 11:36 AM
SpringFan25
Your method for finding the CDF is correct(but i didn't check you did the integral properly).

the 10 percentile $x_{10}$ satisfies:

$F(x_{10}) = 0.1$
• June 7th 2010, 11:46 AM
losm1
I'm little bit confused with notation $x_{10}$, can you write complete calculation pls?
• June 7th 2010, 12:03 PM
SpringFan25
i have just called the 10th percentile $x_{10}$

The definition of a percentile is:

$P(X
$F(x_{10}) = 0.1$

So find the value of x that satisfies

$2x^2 - x^4 = 0.1$

Can you finish from there?

Hint: this is a quadratic in $x^2$
• June 7th 2010, 12:16 PM
losm1
Ok, thanks. So we take a root that is in interval $0 (we have 4 solutions, one in that interval)?
• June 7th 2010, 12:28 PM
SpringFan25
yes, since x can not be outside that interval