Book 1_Quan_PROBABILITY TREES AND CONDITIONAL EXPECTATIONS

Question 1

The expected value of a random variable

Answer 1

the weighted average of its possible
outcomes:
E(X) = ΣP(xi)xi = P(x1)x1 + P(x2)x2 + … + P(xn)xn

Question 2

Variance

Answer 2

be calculated as the probability-weighted sum of the squared
deviations from the mean or expected value.

Question 3

The standard deviation

Answer 3

the positive
square root of the variance.

Question 4

A probability tree

Answer 4

shows the probabilities of two events and the conditional probabilities of two subsequent events:

Question 5

Conditional expected values

Answer 5

+ depend on the outcome of some other event.
+ Forecasts of expected values for a stock’s return, earnings, and dividends can be refined, using
conditional expected values, when new information arrives that affects the expected
outcome.

Question 6

Bayes’ formula

Answer 6

Bayes’ formula for updating probabilities based on the occurrence of an event O is as
follows
P(I/O) = P(O/I)/P(O) x P(I)

Equivalently, based on the following tree diagram,
P(A/C) = P(AC)/(P(AC)+P(BC))