I How do I find the expected value and median of a probability density function?

khansen9
Messages
1
Reaction score
0
TL;DR Summary
TL;Integral
Hey everyone, I have been struggling to find the expected value and median of f(x) = 1/2e^-x/2, for x greater than 0. I am just wondering how I do so? Thank you.
 
Physics news on Phys.org
What are the definitions of the expectation and the median for a continuous random variable? :smile:
 
If f(x) is supposed to be a probability density, then it has to be normalized so its integral = 1.
 
For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...
Back
Top