# 2/20/2023

## Problem Session (QQ plots and Binomial Distributions)

- 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)

- 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.

##