1. ## find variance

Fx(x)= 0 , x<1
Fx(x)= (x^2-2x+2)/2 , 1<= x <2
Fx(x)=1, x>=2

calcualtae the variance of x.

I drew the graph of this function. it is a mixed distribution with a point-mass at 1. But i dont know how to solve it.....

2. Hello,

Find the pdf f of this function, by differentiating $F_X$

Then the variance is :
$\int_0^2 x^2 f(x) ~dx-\left(\int_0^2 x f(x) ~dx\right)^2$
(definition of the variance)

3. Almost (certainly, not).
You're slipping, moo, you need the square.

Originally Posted by Moo
Hello,

Find the pdf f of this function, by differentiating $F_X$

Then the variance is :
$\int_0^2 x^2 f(x) ~dx-\left(\int_0^2 x f(x) ~dx\right)^{\color{red}2}$

This is the short cut formula for the variance.

The definition is $E\biggl(X-E(X)\biggr)^2$