Midterm 2

Question 1

The Expected Values

Answer 1

Let X be a RV defined for the outcomes in a sample space S

E(X)= Sum(x*P(X=x))

Question 2

Binomial RV

Answer 2

nCkp^(k)q^(n-k)
where p is success and q is failure (1-p)
E(X)=np

Question 3

Linearity of Expectations

Answer 3

E(aX)=aE(X)
E(X+Y)=E(X)+E(Y)

Question 4

Independent RV

Answer 4

E(XY)=E(X)*E(Y)

Question 5

Geometric Distribution

Answer 5

P(T=k)=p(1-p)^(k-1)

E(T)1/p

Question 6

Conditional Probability

Answer 6

P(A|B)=P(A^B)/P(B)

Question 7

Bayes’s

Answer 7

………………………. ** (P(E|F).P(F))**
…..P(F|E)= __________________________
………………(P(E|F).P(F)+P(E|Fc).P(Fc)

Question 8

Bayes’s shortcut

Answer 8

………………..P(E|F).P(F)
P(F|E)=_____________________
…………………P(E)