QM LM4 Probability trees and conditional expectations

Question 1

Why do we care about probability?

Answer 1

Investment decisions are made under uncertainty

Question 2

How do we calculate expected value using a probability tree?

Answer 2

• Multiply probability of every branch of the tree with the associated value
• Sum them together

Question 3

How do we calculate variance of an expected value using a probability tree?

Answer 3

• Calculate the expected value by multiplying probability of every branch of the tree with each associated value, and summing them together
• Take the difference of each outcome from the expected value, square it, and multiiply by the probability of that outcome
• Add these together

Question 4

What is Bayes’ formula>

Answer 4

• A method for updating prior probabilities based on new information
• Tells us how we should modify our prior probabilities based on an event to create new posterior probabilities

Question 5

How do we calculate any prior probability that an event has occured given an outcome using Bayesian theorem?

Answer 5

• Find the known event that we have observed from the probability tree on the arm of the unknown event
• Multiply the probability along the tree to the known event on that arm
• Divide by the total of probabilities of the known event occuring, including the unknown event not happening
• This will give you the probability that the unknown event has occured given the known event