Originally Posted by
somestudent2 Given: Suppose that a R.V Y has a probability density function by:
f(y) = k * (y^3) * e^(-y/2) when y > 0
f(y) = 0 elsewhere
a) Find the value of k that makes f(y) a density function:
b) What are the mean and standard deviation of Y?
Sol.
For part a) I started out the same way as in previous similar problem.
I integrate f(y)=k*(y^3) * e^(-y/2) from 0 to infinity and make it equal to 1. I get this:
-2 k (48 + x (24 + x (6 + x)))
------------------------------
e^x/2
If we solve it from 0 to infinity it comes out to be 0... I checked the integral with a computer program, it looks right. I wonder maybe it should be from 1 to infinity? Then it is possible to find k.