Can I Justify This Yes/No Question?

[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?

 

[dikmikkel]

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

 

[Ray Vickson]

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?

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