1/15/2024

Introductions

Course Roster

Course Web Page

Syllabus

Overview of the course

• Estimation
• Inference (intervals and testing)
• Simulation (Look at Applets)

Estimation Activity

• Number of popsicle sticks (Famous German tank problem)
  • Each group takes a sample (without replacement) of 3 sticks from the container.
  • Determine an estimate of N.
  • Describe your rule or formula for the estimator of N based on a sample size of n.
• Number of jelly beans in a jar
  • Use the output from statistical software to estimate the number of jelly beans in a jar.
• Evaluating estimators:
  • The class must decide which estimator to use.
  • How would you suggest that we decide which estimator is best?
  • What graphical displays and descriptive statistics would you use to compare the estimators?

Group Activity - Review

• Moment generating function (m.g.f.)
  • Find the m.g.f. of a standard normal random variable Z
• If Z is a standard normal random variable, find the distribution of X = mu + sigma*Z.
• Use the m.g.f. to show that a linear transformation of a normal random variable will also have a normal distribution.
• Use the m.g.f. to show that the sum of independent normal random variables will also have a normal distribution
• Simulation with R
  • Simulate the distributions of the mean and median for Normal data.
  • Simulate the distributions of the mean and median for Cauchy data.
  • Simulate the distributions of the standard deviation and the range.

Please read Section 6.5 and Chapter 7 for class on Wednesday