# Probability Density Function

• Apr 4th 2011, 10:21 PM
jzellt
Probability Density Function
Suppose that a random variable Y has a probability density function given by

f(y) = {6y(1-y), 0 <= y <= 1 AND 0 elsewhere}

a)Find F(y)
b)Graph F(y) and f(y)
c)Find P(.5<=Y<=.8)

Thanks for any help!!
• Apr 4th 2011, 11:55 PM
CaptainBlack
Quote:

Originally Posted by jzellt
Suppose that a random variable Y has a probability density function given by

f(y) = {6y(1-y), 0 <= y <= 1 AND 0 elsewhere}

a)Find F(y)
b)Graph F(y) and f(y)
c)Find P(.5<=Y<=.8)

Thanks for any help!!

$\displaystyle F_Y(y)=\int_{-\infty}^y f_Y(\zeta)d\zeta$

where:

$f_Y(y)=\left\{ \begin{array}{ll}6y(1-y),& 0 \le y \le 1 \\ \\ 0, & \text{otherwise}\end{array} \right.$

Now what exactly is the problem you are having with this?

CB
• Apr 5th 2011, 11:58 PM
matheagle
This is a $\beta(2,2)$ by the way.

That's why the $\Gamma(4)=6$ is your coefficient.