[Lign251] HW3 Q3

[rlevy at ling.ucsd.edu]

Rebecca Colavin wrote:
> Okay, I give up.
>
> The graph in the question generates a distribution where the probability

> mass (=1) is contained under the curve. In short, the y axis is (0,9) or

> so .
>
> But when I try to do lines over it with a normal distribution, the y 
values are probabilities. The y axis for this is (0,1).

Hi Rebecca,

Because the normal distribution is a continuous probability density, the 
y values (for the density) are not bounded above by 1.  Remember, it is 
the *area under the curve* that must total 1.  If the scale of the x  axis
is small, p(x) can easily surpass 1.

As an example, try:

 > x <- seq(-5,5,by=0.01)
 > plot(x,dnorm(x,0,0.1),type="l")

This normal density peaks around p(x) = 4.

Using hist() with prob=T also is an estimation of density, which is why 
the hist() y axis also surpasses 1.


Roger


-- 

Roger Levy                      Email: rlevy at ucsd.edu
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