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)
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