I have 2 curves illustrated with the following Mathematica code:
Show[Plot[PDF[NormalDistribution[0.044, 0.040], x], {x, 0, 0.5}, PlotStyle -> Red],
Plot[PDF[NormalDistribution[0.138, 0.097], x], {x, 0, 0.5}]]
I need to do 2 things:
- Find the x and y coordinates where the two curves intersect and
- Find the area under the red curve to the right of the x coordinate in the above intersection.
I haven't done this kind of problem in Mathematica before and haven't found a way to do this in the documentation. Not certain what to search for.
Can find where they intersect with Solve (or could use FindRoot).
Out[4]= 0.0995521
Now take the CDF up to that point.
Out[5]= 0.917554
Was not sure if you wanted to begin at x=0 or -infinity; my version does the latter. If the former then just subtract off the CDF evaluated at x=0.
FindRoot usage would be
Out[6]= 0.0995521
If you were working with something other than probability distributions you could integrate up to the intersection value. Using CDF is a useful shortcut since we had a PDF to integrate.
Daniel Lichtblau Wolfram Research