9/20/2023

Chapter 4 - Expectation and more with discrete random variables - see Chapter4 - Expected Value.pdf

• Probability mass function
  • Common notation - m(x) or p(x) or f(x)
  • See the bottom of p. 126 for the p.m.f.s of the Bernoulli, Binomial, Poisson, and Uniform
• Expected value
• Properties of expected value
• Expected value for a function of a random variable
  • General form
  • Linear function
• Joint distribution
• Marginal distribution
• Expected value of two random variables
• Expected value for independent random variables
• Sums of random variables
• Expected value for sums of random variables - linearity of expectation
• Indicator variable
• Expected value of an indicator variable
• Variance and standard deviation
• Properties of variance and standard deviations
• Variance of sums
• Covariance and correlation
• Properties of covariance and correlation
• Conditonal distributions
• Conditional expected value
• R code for expected values - see R Supplement for Chapter 4
  • Discuss this code with a partner
• Lab time for working with R and solving the HW exercises for Friday

We will have a problem session on Friday.