How To Find The Median And Variance?

**AlphaRock** · March 21st 2010, 03:48 PM

Can somebody show me how to find the median and variance of this piece wise function? I've been trying so hard to do it.

f(x) =
4/(x^5) , x >= 1
0, otherwise

Ans: 1.11, 7/9

**Moo** · March 21st 2010, 05:18 PM

Hello,

Compute the cdf :

F(t)=0 if t<1
$F(t)=\int_{1}^t 4x^{-5}~dx=1-\frac{1}{t^4}$ if t>1

The median is the value m such that $F(m)=0.5$ . Shouldn't be too difficult...

The variance is $E[X^2]-E[X]^2=\int_1^\infty x^2f(x) ~dx-\left(\int_1^\infty xf(x) ~dx\right)^2=\dots$

Note : the fact that it is piecewise is not that important. Here, it just tells you the range of the distribution.

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