Hey,

Can anyone help me with the following question:

f(x) = K(1+x)^n such that x>0

and

f(x) = 0 otherwise.

for some constants K and n.

For what values of n can f be made into a valid probability density?

Any help would be greatly appreciated.

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- Feb 23rd 2006, 09:37 AMjedoobprobability density function
Hey,

Can anyone help me with the following question:

f(x) = K(1+x)^n such that x>0

and

f(x) = 0 otherwise.

for some constants K and n.

For what values of n can f be made into a valid probability density?

Any help would be greatly appreciated. - Feb 23rd 2006, 10:26 AMCaptainBlackQuote:

Originally Posted by**jedoob**

,

for some and .

For what values of can be made into a valid probability density.

Now is a probability density if and only if for all , and

.

Now the integral is infinite when , and if :

.

Now as otherwise would not be be

greater than or equal to zero. Then , which can only

be made to work if .

RonL - Feb 23rd 2006, 10:46 AMjedoobThanks
Thanks a million.