

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 

Probability Old Exam P Forum 

Thread Tools  Search this Thread  Display Modes 
#1




Help with Gamma Random Variable Problem
Hi,
I run into this problem when I'm studying: Suppose the continuous random variable X has the following pdf: f(x) = (1/16)*(x^2)*e^(x/2) if x > 0 0 otherwise Find E(X^3). Clearly the λ = 1/2 and α = 3, but I don't know how to solve it other than going through the complicated integration. Is there any good way to solve it? 
#4




You want to calculate the third moment. That means integrating x^3 f(x). Notice that x^3, when multiplied by x^2, becomes x^5. So you're integrating x^5 e^{x/2} times some constant. That looks like a gamma density function, doesn't it? And gamma density functions got to integrate to 1. So just figure out what the constant in the density function is and voila  the integral of x^5 e^{x/2} got to be the reciprocal of that constant!

Tags 
gamma random variable, help!, pexam 
Thread Tools  Search this Thread 
Display Modes  

