# Probability function p(x) if p(10) = p(20), do any x values lie between 10 and 20?

1. Apr 15, 2012

### IntegrateMe

This is a yes/no question. Though I feel that being able to justify it is more important than getting the answer correct. Can anyone help me figure this one out?

2. Apr 15, 2012

### dikmikkel

Re: Probability function p(x)...if p(10) = p(20), do any x values lie between 10 and

How about considering the normal distribution shape. There it is symmetric about 0. So in general the answer is yes.

3. Apr 15, 2012

### Ray Vickson

Re: Probability function p(x)...if p(10) = p(20), do any x values lie between 10 and

It all depends on what p(x) is supposed to mean. (i) Is it a probability density function of a continuous random variable? (ii) Is it a probability mass function of a discrete random variable defined on the integers? (iii) Is it a cumulative distribution function?

In both (i) and (ii) the answer is: yes in some examples and no in other examples (although getting a "no" for a continuous random variable involves using a discontinuous density function with jumps at x = 10 and at x = 20, and supposing the density to be actually give a finite value at those two points---to which some might object). In (iii) the answer is a definite no: there are no other values between 10 and 20.

RGV

Last edited: Apr 15, 2012