Here is some of my work on Matlab and an actuarial exam P study manual

What is the expectance of E(X+Y+Z)^2 if mean is 3 for x,y,z exponentional variables

syms x y z

fx(x)=(1/3)*exp(-x/3)

fy(y)=(1/3)*exp(-y/3)

fz(z)=(1/3)*exp(-z/3)

expand((x+y+z)^2)

Ex1=int(x*fx(x),0,inf)

Ex2=int(x^2*fx(x),0,inf)

E2xy=int(int(2*x*fx(x),0,inf) * y * fy(y),0,inf)

E2xz=int(int(2*x*fx(x),0,inf) * z * fz(z),0,inf)

Ey2=int(y^2*fy(y),0,inf)

E2yz=int(int(2*y*fy(y),0,inf) * z * fz(z),0,inf)

Ez2=int(z^2*fz(z),0,inf)

Etrinomialnis2=Ex2+E2xy+E2xz+Ey2+E2yz+Ez2

What is the P(Y>1/2) given 0 < x < y < z < 1 ?

syms x y z

fz(z)=z

fx(x)=x

fy(y)=y

int1=int(48*fz(z),y,1)

int2=int(int1*fx(x),0,y)

int3=int(int2*fy(y),1/2,1)

double(int3)

(My favorite) What is the expectance of X and Y=5, given Y=5?

X is distributed as the first time a 6 appears on a fair die

Y is distributed as the first even number appearing on another fair die

syms x y

fx(x)=(5/6)^(x-1)*(1/6)

fy(y)=(1/2)^(y-1)*(1/2)

den=double(int(y * fy(y),0,5))

num=int(x * den * fx(x),0,inf)

ans=round(num/den)