why are some distribution's pdf greater than 1 at some points x?

an example,

>>pf=ProbDistUnivParam('rayl',0.4);
>> x=-10:0.001:10;
>> plot(x,pdf(pf,x));

(i cannot insert an image here, sorry...)

plot the pdf of Rayleigh Distribution, obviously , pdf'value is greater than 1 at x=0.5 around.

why?

[Image Analyst]

http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

Answer 1

[the cyclist]

The integral of a valid pdf must be equal to 1, but that doesn't mean the pdf itself can't be greater than 1 for some values of x. For example,

p(x) = 2 when x > 0 and x < 0.5
     = 0 otherwise

is a valid pdf.