# Thread: Percentiles in a Continous Random Variable distribution

1. ## Percentiles in a Continous Random Variable distribution

The probability density function of x is:
f(x) = 4x(1-x^2) when x is a value between 0 and 1. (0 and 1 are included)
= 0 otherwise
What is the 75th percentile of this distribution?

2. the 75th percentile is the the x that gives the answer f=0.75 I believe

3. Originally Posted by Pink Lady
The probability density function of x is:
f(x) = 4x(1-x^2) when x is a value between 0 and 1. (0 and 1 are included)
= 0 otherwise
What is the 75th percentile of this distribution?
By definition:

Find the value of a such that $\int_0^a 4x (1 - x^2) \, dx = 0.75$.

Originally Posted by Flyingdutchman
the 75th percentile is the the x that gives the answer f=0.75 I believe
Sorry but that's not correct.

4. It's F(a)=.75, not f(a)=.75.

5. $P(X \leqslant a) = \left\{ {\begin{array}{*{20}c}
{0,} & {a \leqslant 0} \\
{\int_0^a {4x(1 - x^2 )dx,} } & {0 < a \leqslant 1} \\
{1,} & {1 < a} \\ \end{array} } \right.$