pdf at a single point

Hi all,

A probably very silly question:

since the probability that a normal random variable X equals any particular value is zero, how come, for example, normpdf(0.421) does not return zero?

Cheers!

Answer 1

[Wayne King]

Don't confuse the value of the PDF at a point with the probability that the random variable takes on that value. Those are different things. The probability that the random variable takes on any single value is the integral of the PDF with the lower and upper limits of integration the same (the value) and hence that is always zero.

[Wayne King]

What you want to verify is always zero is (for example):

x = 2; % or any value

normcdf(x,0,1)-normcdf(x,0,1)

[Lucas]

I understand. Thanks a lot!

Just one clarification:

If I am comparing two normal distributions, say, height of men and women and I want to know if height = 1.9m is more likely to be drawn from the men's distribution. It makes sense to compare the value of the pdf's at this point (normpdf outputs), although the probability of the pdf's assuming the value of 1.9 is zero, right?