2/18/2022

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.