11/6/2023

Chapter 7 - Continuous Distributions continued

See Chapter7 - Chi-squared distribution.pdf in our Google Drive folder

• Chi-squared distribution
  • Derivation of this special case of the gamma distribution
  • Show that the sum of chi-squared random variables stays in the chi-squared family
  • Calculating probabilities, finding percentiles, and generating random observations for chi-squared distributions
    • dchisq(k, df), pchisq(k, df), qchisq(k, df), and rchisq(n, df) with RStudio

• t distribution
• General discussion about the form and derivation of the pdf
• Calculating probabilities, finding percentiles, and generating random observations for t distributions
  • dt(k, df), pt(k, df), qt(p, df), and rt(n, df) with RStudio

• F distribution
• General discussion about the form and derivation of the pdf
• Find the mean
• Calculating probabilities, finding percentiles, and generating random observations for F distributions
  • df(k, df1, df2), pf(k, df1, df2), qf(p, df1, df2), and rf(n, df1, df2) with RStudio

Class Activity or Live Coding.

• Use RStudio to find the 5th percentile for a chi-squared distribution with 3 degrees of freedom.
• Find the probability that a chi-squared random variable with 3 degrees of freedom is greater than 2.
• Find the IQR for a t distribution with 1 degree of freedom
• Find the 95th percentile for a t distribution with 10 degrees of freedom. Increase the degrees of freedom by 10, then 100, then 1000 and find the 95th percentiles of these t distributions. What value does the 95th percentile converge to? Be specific.
• Create an example in RStudio that illustrates the relationship between the pth quantile for an F(m, n) and the (1-p)th quantile for an F(n, m) distribution.

Please read Chapter 8 for class on Wednesday.