reading 4

• What is the expected value of a random variable?

  The weighted average of possible outcomes
• How is the expected value mathematically represented for a random variable X?

  As a weighted average of values from x1 to xn
• How do you calculate the expected earnings per share (EPS)?

  • Weighted average of each possible EPS
  • Weights are the probabilities of outcomes
• What do variance and standard deviation measure in a random variable?

  The dispersion around its expected value
• How is variance calculated from a probability model?

  As the probability-weighted sum of squared deviations
• What is the standard deviation in relation to variance?

  The positive square root of the variance
• What is the process to calculate expected return, variance, and standard deviation for Stock A?

  1. Calculate expected return as probability-weighted sum
  2. Find differences from expected return
  3. Square the differences
  4. Multiply probabilities by squared deviations
  5. Sum to find variance
  6. Take square root for standard deviation
• How is the sample standard deviation different from the standard deviation from a probability model?

  Sample standard deviation uses n-1 for calculations
• What is a probability tree used for in investment applications?

  To show probabilities of various outcomes
• How can expected EPS be calculated using a probability tree?

  By summing the weighted outcomes of EPS
• What must the probabilities of possible outcomes in a probability tree sum to?

  1
• What are conditional expected values based on?

  On the outcome of some other event
• How does a tariff on steel imports affect the conditional expected return of a stock?

  It increases the conditional expected return
• What is Bayes’ formula used for in probability?

  To update prior probabilities with new information
• How is Bayes’ formula derived?

  Using the multiplication rule of probabilities
• What does the joint probability in Bayes’ formula represent?

  The probability of two events occurring together
• What is the process to calculate updated probabilities using Bayes’ formula?

  1. Identify prior probabilities
  2. Determine conditional probabilities
  3. Apply Bayes’ formula
  4. Calculate updated probabilities based on new information
• What is the unconditional probability P(B) in Bayes’ formula?

  The total probability of event B occurring
• Given a stock increased in value, how do you calculate the probability that the economy outperformed?

  By summing probabilities of gains in both states
• What are the key concepts related to expected value, variance, and standard deviation?

  • Expected value: weighted average of outcomes
  • Variance: probability-weighted sum of squared deviations
  • Standard deviation: square root of variance
• What are the key concepts related to probability trees and conditional expectations?

  • Probability trees show event probabilities
  • Conditional expected values depend on other events
  • Forecasts can be refined with new information
• What are the key concepts related to Bayes’ formula?

  • Updates prior probabilities with new information
  • Derived from multiplication rule
  • Calculates joint probabilities of events
• What is the expected value of X given the conditional probabilities in the module quiz?

  5.3
• What is the updated probability that Davies Company’s EPS are greater than $2?

  60%
• What is the answer key for Module Quiz 4.1 regarding expected value?

  B (LOS 4.a)
• What is the answer key for Module Quiz 4.1 regarding updated probability?

  C (LOS 4.c)