MATLAB: How to Calculate the PDF and CDF of a product of two i.i.d exponentially distributed random variables with mean a and b respectively

exponential

You get

F(x)=1-2*sqrt((lambda1)*(lambda2)*x)*K1(2*sqrt((lambda1)*(lambda2)*x))
f(x)=2*(lambda1)*(lambda2)*K0(2*sqrt((lambda1)*(lambda2)*x))

with

lambda1 = 1/m

lambda2 = 1/n

K0, K1 : Modified Bessel functions of the second kind

Best wishes

Torsten.

z = a*x+b*x^2+c+........; 
eqn = subs(sym('D2y +5*z+ 2*x + 10*z^2'), z, z);
S = dsolve(eqn, x);

Myself, I would probably toss in a simplify() around the subs() .

The density function for X+Y is given by

f_X+Y(z)=exp(-q*z)*p^(2*m)/(gamma(m))^2*integral_{x=0}^{x=z}(x*(z-x))^(m-1)*exp(-(p-q)*x) dx

Use MATLAB's "integral" to evaluate the integral for different values of z.

Best wishes

Torsten.