Probabilities Flashcards
1
Q
Odds for A
A
P(A)/1-P(A)
2
Q
Odds against A
A
1-P(A)/P(A)
3
Q
P(A|B)
A
P(A|B)=P(AB)/P(B)
P(AB)= P(A|B) x P (B)
4
Q
Indep Probability
Expected Values Xn
A
ĘP(Xn) x Xn
5
Q
Var(x)
A
= E[(x - E(x))^2]
Or
= ĘP(xi)[xi- E(x)]^2
6
Q
E (X|S)
A
E(X|S) = P(x1|S)x1 + P(x2|S)x2 ….
E(x) = E(X|S) P(S) + E(X|S’) P(S’)
7
Q
E(Rp)
A
E(Rp) = w1E(Ri) + w2E(Ri) …
8
Q
Var(Rp)
A
Var(Rp) = ĘĘwiwjCov(Ri, Rj)
9
Q
Cov (RiRj)
A
Cov(Ri,Rj) = Correl(Ri,Rj)/st dev(Ri) x st dev (Rj)
10
Q
Joint prob of portfolio
A
P(RaRb) [(Ra - E(Ra)) x (Rb - E(Rb))]
11
Q
Var(Rp)
A
Var(Rp) = w1^2 Var(R1) + w2^2 Var(R2) + 2w1w2Cov(R1R2)
12
Q
E(X)
A
E(x) = E(x|S)P(S) + E(x|S’)P(S’)
Whereas
E(x|S) = ĘP(Xn|S)Xn +….
13
Q
Bernulli
A
P(x) = nCk p^k (1-p)^n-k
14
Q
Bayers formula
A
P (S|E) = P(E|S)/P(E) x P(S)
Whereas
P(E) = P(E|S)P(S) + P(E|S)P(S’)
