problems with plotting density function

Hi, I have 2 dimensional distribution where one dimension are random binary numbers and the other are random real numbers with support [-2,2]. So the data looks like this:

    1.0000   -1.3044
    1.0000   -0.5507
    1.0000   -1.0699
    1.0000   -1.3371
    1.0000    0.7970
    1.0000   -0.4662
         0   -0.7049
         0    0.0364
         0   -1.0314
    1.0000    0.0046

Lets call first column x and second y. I'm interested in plotting objects P(x=1|y<Y) and corresponding density (as functions of Y). I can plot cdf Prob(x=1|y<Y) as function of Y, but I'm having problems with plotting corresponding density. I have tried to do something like this:

m=100;
xpv=linspace(-2,2,m);
for i=2:m 
    pdf_e(i)=(cdf(xpv(i)h)-cdf(xpv(i-1)))/(xpv(i)-xpv(i-1));
end

where cdf(a) = Prob(x=1|y<a) but it gives me something really strange. (cdf function works fine by the way).Can someone please help me with this.

Thanks, Kenan

Answer 1

[Roger Stafford]

In terms of the numerical quantities matlab is dealing with, it is not possible to define a probability density for a discrete-valued variable. The 'density' would have to be infinite in this case at x = 0 or 1 and zero for other values of x but such that its integral with respect to x is 1, in much the same manner as is true with the dirac delta "function". This is something beyond matlab's numerical capabilities and belongs to what is known as "measure theory", so you should not attempt the kind of computation you describe with ordinary arithmetic operations. As you have discovered, they wouldn't make any sense.