LF1 and LF2 return quite different numbers, and only that of LF2 agrees with theoretical results and computations done with other packages. What do I do wrong, or how do I optimise correctly, only knowing that p in (0,1) and lambda >0? Is there anything more appropriate than NLPSolve?

I was trying to extend these www.mapleprimes.com/forum/probfunctioneasytaskfailed ideas to compute the ratio distribution function of two r.v.'s, something along these mathworld.wolfram.com/RatioDistribution.html lines. So how do I do that with Maple, say for the ratio of two independent zero-trancated Geometrical r.v.'s? Or how do I obtain with Maple the distribution of the reciprocal of such a random variable?Thanks.

What's the standard (or a cool non-standard)  way to compute the expected value of a matrix, e.g., a covariance matrix? Using this code:

restart; with(LinearAlgebra): e1 := Statistics:-RandomVariable(Normal(0, sigma)); L := [seq(e1*cos(pi*t), t = 1 .. 3)]; convert(L, Matrix); Transpose(convert(L, Matrix)); M := Multiply(%, %%); S := map(Statistics:-Mean, M)

how do I simplify S to the matrix of +/- one's and factor out sigma^2 outside the matrix? Thanks. 

 

How do I use ProbabilityTable so that the first element in P denotes the probability of zero, and not one? That is I have three states: 0,1, and 2, and I want them be an immediate output of my Sample. Thanks.

with(Statistics):
P:= [1/2,1/8,3/8];
X:= RandomVariable(ProbabilityTable(P));
ProbabilityFunction(X, 0);
Sample(X, 10);
 

How do I get expressions 2.3 to 2.5 from this old paper: projecteuclid.org/DPubS with maple? What is the standard (or otherwise) way to compute (symbolically)  this sort of thing with Maple, e.g., using intersect, assuming?  Nothing seems to work for me. Thanks.