expected value, uniform distribution

[anavia]

Hi everyone,

i have a weird question and here it goes,

if x is uniformly distributed within the region (0,1]. How should I find

E [(A + Bx^2)^{1-m}]

where A>0, B>0 and 1>m>0 are constants and E (.) is the expectation operator?

Could someone help? I appreciate any answers :) or if you could help me with some suitable literature, it would be also very nice.

[Dragan]

Hi everyone,

i have a weird question and here it goes,

if x is uniformly distributed within the region (0,1]. How should I find

E [(A + Bx^2)^{1-m}]

where A>0, B>0 and 1>m>0 are constants and E (.) is the expectation operator?

Could someone help? I appreciate any answers :) or if you could help me with some suitable literature, it would be also very nice.



You're right it is a rather weird question.


In general, when you integrate the function (to get the expected value) it is going to involve the solution of a hypergeometric differential equation.

To evaluate the integral to get an exact solution for the expected value you can use the Mathematica function:

A^{1-m}\textup{Hypergeometric}2F1\left \{ \frac{1}{2},m-1,\frac{3}{2},-\frac{B}{A} \right \} .


For example, if A = 10, B = 5, and m = 1/4, then the expected value is 6.303221...