10/4/2021

Questions on Normal Distributions, especially calculations with RStudio

Binomial Experiments (A generalization of the discrete RV lab problem on the number of patients who experience side effects)

• Each random trial can result in one of only two possible outcomes.  This is called a Bernoulli trial.
• We collect data from Bernoulli trials satisfying the following:
  • there are n trials;
  • the n trials are independent; and
  • the probability of “success” remains constant from trial to trial.
• Binomial Distribution - If X is the number of successes in n independent Bernoulli trials, then P(X=k)=n!/[k!*(n-k)!]*p^k*(1-p)^n-k, for k=0, 1, ..., n.
• Using RStudio for Binomial Probability Calculations 
  • dbinom() or pbinom() or qbinom()

The mean (expected value) and standard deviation of a binomial random variable

• Mean (or Expected Value) of X is n*p
• Variance of X is n*p*(1-p)
• The standard deviation of X is the square root of the variance.

Binomial Random Variables - See handout

Please read Sections 4.4 and 4.5 for class on Monday.

Reminder: Our first exam covering Chapters 1, 2, 3, and Sections 4.1-4.3 will be on Wednesday, October 6. You may prepare three note sheets (8.5"x11") to use druing the exam. You will also be allowed to use our course web page and RStudio during the exam.