3. Exact and Asymptotic Sampling Distributions

Topics, Class Notes and Code Assignments and Recommended Readings
  • Sampling Distribution of Sample Means
    • Exact distribution
      • Normal population with known variance
      • Normal population with unknown variance
    • Asymtotpic distributions (CLT)
  • Sampling distribution of sample proportions
  • Sampling distribution related to sample variances of normal populations
    • Single variance: $(n-1)s^2/\sigma^2 \to \chi^2_{n-1}$
    • ratio id two sample variances: F distribution
  • Notes and code
  • Base R Functions for Distributions
    • Normal distribution: rnorm(), dnorm(), pnorm(), pnorm()
    • t Distribution: rt(), dt(), pt(), qt()
    • $\chi^2$ Distribution: rchisq(), dchisq(), pchisq(), qchisq()
    • F Distribution: rf(), df(), pf(), qf()
  • Assignment #2: Write a short essay describing the normal, t, chi-square, and F distributions, their assumptions, and their connections.
  • Due:Tuessday. 2/10/2026 at 11:30 PM,