RVs2

Question 1

When is RV X integrable

Answer 1

RV X is integrable when E(mod(x)) < inf
E(X) = E(X+) - E(X-)
Denoted L’

Question 2

What are the +I’ve and -I’ve parts of an RB

Answer 2

+I’ve part of an RV is X+(w) = max( 0, X(w))
-I’ve part of an RV is X-(w) = max (0,-X(w))
X = X+ - X-

Question 3

What is mod(E[X]) <= to

Answer 3

Mod(E[X]) <= E[mod(x)]

Question 4

What is E[LX + UY]

Answer 4

E[LX + UY] = LE[X] + UE[Y]

Question 5

What is E[h(X)] with h: X(omega) to R and when is h integrable

Answer 5

E[h(X)] is sum x in X(omega) h(x)P(X=x)
H is integrable iff sum is absolutely convergent

Question 6

What is E[h(X)] if h and X are continuous

Answer 6

E[h(X)] is integral over R h(x) fx (r) dr

Question 7

What does the bounded convergence theorem state

Answer 7

Bounded convergence theorem states that:
If Xn , n>= 1 and X be RVs s.t Xn tends to X so P(Xn tends to X) = 1.
Assume mod(Xn) is finite
Then E[mod(Xn - X)] tends to 0 and E[Xn] tends to E[X]