We simply place the values into the formula for the variance:
Var(Rp) = 0.902* 0.0011 + 0.102* 0.016 + 2 * 0.9 * 0.10 * (-0.0036).
Var(Rp) = 0.000403
Since options are a zero-sum game, we might assume E(RO) = 0. Then the expected return of the portfolio is 0.9 * E(RS).
t: Calculate an updated probability, using Bayes' formula.
Bayes' formulasays that given a set of prior probabilities for an event of interest, if you can receive new information, the rule for updating the probability of the event is:
Updated probability =
Probability of new information given event
x
Prior probability of event
Unconditional probability of new information