10/11/2021

Discussion of Exam #1

Geometric Distribution

• Waiting for the first success in a sequence of Bernoulli trials
• If X is the number of Bernoulli trials in order to get the first success, then P(X=k)=(1-p)^k-1*p, for k=1, 2, ....
• Using RStudio for Geometric Probability Calculations 
  • dgeom(x, p)
  • pgeom(x, p)
  • qgeom(q, p)
• You can also use the visualize library
  • library(visualize)
  • visualize.geom(stat=1, prob=0.3, section="lower", strict = FALSE)

The mean, variance, and standard deviation of a geometric random variable

• Mean = 1/p
• Variance = (1-p)/p^2
• Standard deviation = sqrt((1-p)/p^2)

Negative Binomial Distribution

• Waiting for the kth success in a sequence of Bernoulli trials
  • The trials are independent
  • Each trial outcome can be classified as a success or a failure
  • The probability of a success (p) is the same for each trial
  • The last trial must be a success
• Use nbinom in R

Class Exercises

4.13, 4.27, 4.29

Please read Section 4.5 for class on Wednesday.