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!!

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- Apr 4th 2011, 09:21 PMjzelltProbability 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, 10:55 PMCaptainBlack
Let's start with a).

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

where:

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

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

CB - Apr 5th 2011, 10:58 PMmatheagle
This is a $\displaystyle \beta(2,2)$ by the way.

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