DSE 2007

[Rain Man]

Q :
A continuous random variable has the probability density function f(x) = 1/3 , for x between -1 and +2 , and 0 elsewhere . Its mean , variance and median are :

Here , how do we calculate the variance and median .

please help

thanks

[sonudelhi]

this is quite easy
calculate E(X)=1/2
then E(X2)=1

now use var(X)=E(x2)-[E(x)]2=1-1/4=3/4

[sweta]

@sonudelhi
 hi can u tell me how do we get E(X)=1/2 here

[Chocolate Frog]

Sweta, you need to integrate xf(x) from -1 to 2.

Rain Man, for median, you need to find a point x such that P(X>=x) >= 1/2 and P(X=<x) >= 1/2. Since we have a uniform distribution, x is easily seen to be the midway point, or 1/2.