I have a random variable called Y1, which looks like the following: Y1 = 2*sqrt(1 - x^2)/Pi, on the (-1 < x < 1) interval. This "semicircle" integrates to 1, like other random variables. Random variable Y2 is the same as Y1 above. I want to find the random variable Z, which is equal to the absolute difference of two random variables Y1 and Y2. In other words, I want to find Z = |Y1 - Y2|. Via simulation, I know that |Y1 - Y2| takes on a logrithmic form, but I need to get a mathematical solution of this.

I am interested in determining the density function which results from multiplying two random variables.  I have read about the Mellin Transformation, but I just end up confused.  I have two random variables:  f[1], which is nonzero on the 0 < t < 2 interval, and f[2], which is nonzero on the 0 < t < 1 interval.  Of course, both of these random variables sum to one when evaluated.

Any thoughts on how I can obtain the density function for this?  My work is below.

Download Inquiry.mw

Greetings,

I have generated two random points in the unit square.  Each point has an x and y coordinate.  The density function for the (absolute) distance between each point is (2-2d) in both the x and y direction.  These distances are shown by the "f" and "g" functions attached.

The overall (rectilinear) difference is what I am after.  The attached worksheet shows the rectilinear distance as "h".  

My question is this...how can I obtain this rectilinear distance by using convolution and the "starting" density function of (2-2d) ? 

This is probably more of a mathematics function than a Maple question, but the "rules" of convolution, particularly setting the upper and lower boundaries of the integrals confuse me.

DensityFunction.mw

I constructed a density function, and I am certain it shows me what I want.  The problem I am having is parsing the Elliptic functions. Is there a way to "get rid" of the ones I don't want or need.

I generated a plot of the function -- the plot tells me what I expected based on simulation. I need to know if there is a way to express the density function (y) as a function of t and without the elliptic functions..  Even a numerical solution would be fine.

I assume the denomenator term is correct. I also assume that I don't need complex values. My input file is below.

Basics.mw

I have a piecewise density function (f).  I am trying to find the median value.

I have tried the Median function and the Percentile function, but neither work for me.  I am not sure why.

I have also tried to integrate the density function on the (0,x) interval such that the area under the curve is 1/2 and then solve for x.  This works for simple problems, but not the one attached.

There is something very simple that I'm not doing, but I am not sure what.

Download Median.mw