Expectations Of Variance

Question 1

Properties of expectations of variance (1)

Answer 1

1. If k is constant E(k)=k.
2. Ifk is constant and x a random variable E(kx)=KE(x)
3. If x is a discrete random variable then E(k)=ExP(x)
4. If x and y are random variables then E(x+y)=E(x)+E(y)
5. If a&k are constants and x is a random variable then E(ax+k)=aE(x)+k
6. If f(x) is a random variable and g(x) is a new random variable then Eg(x)=Eg(x)f(x)dx
7. If x is a continuous random variable then E(x)=(xf(x)dx

Question 2

Other properties of expectations of variance

Answer 2

8. If f(x) is a continuous random variable and g(x) is a new variable, then E(x)={g(x)f(x)dx
9. If k is constant then v(k)=0
10. If x is a r.v and k is constant then v(kx)=k^2v(x)
11. If x is a r.v and k&a are constants then v(ax+k)=a^2v(x)
12. If x and y are 2 r.vs then v(x+y)=v(x)+v(y)-2cov(xy)
13. If x and y are 2 r.vs then v(x-y)=v(x)-v(y)+2cov(xy)
14. If x and y are two independent r.vs then v(xy)=v(x).v(y)
15. If x and y are 2 independent r.vs then v(x+y)=v(x)+v(y) or v(x-y)=v(x)-v(y)