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.
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.
A function is defined as follows: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