Divide the joint pdf plane
- From: "huangwen77@xxxxxxxxx" <huangwen77@xxxxxxxxx>
- Date: Fri, 25 Jan 2008 20:24:57 -0800 (PST)
Say I have two independant random variables X and Y follow uniform
distribution, with X~U(0,1) and Y~U(0,2), respectively. Hence, their
joint pdf of X and Y is f(X,Y)=1/2 over a rectangular region on the XY
plane (the four vertices are (0,0), (0,2), (1,2) and (1,0) ). Now I
want to divide the region to two parts S1 and S2 with same area, e.g.,
the straight line X=1/2 or Y=1 both satisfy this requirement. (the
physical meaning behind this is that I want to find a scheme that
chooses X and Y both with probability 1/2, and with the pdf being
uniform in this simple example, the probability is equivalent to
area). The objective of the division is to maximal the sum of the
expectation of Y on S2 and the expectation of X on S1.
A more technical expression can be: given two independant r.v. X and
Y, I want to design a selecting scheme such that I choose X and Y with
equal probability. The reward I got is the value of the chosen r.v.
Now the objective is to maximal the expectation of the reward.
Some natural extension of this problem can be:
(1). Other pdf distribution other than U;
(2). Choosing X and Y with unequal probability (p and 1-p);
(3). Choosing between multiple r.v. (N independant r.v.);
.
- Prev by Date: Re: Simple question.
- Next by Date: how can one compute gamma(x) on a calculator
- Previous by thread: cheap solution manuals
- Next by thread: how can one compute gamma(x) on a calculator
- Index(es):
Relevant Pages
|
