Introduction to Statistics Through Resampling Methods and R, 2nd Edition

Chapter 3

Two Naturally Occurring Probability Distributions

In this chapter, you learn to recognize and describe the binomial and Poisson probability distributions in terms of their cumulative distribution functions and their expectations. You’ll learn when to apply these distributions in your future work along with methods for estimating their parameters using R.

3.1 DISTRIBUTION OF VALUES

Life constantly calls upon us to make decisions. Should penicillin or erythromycin be prescribed for an infection? Is one brand of erythromycin preferable to another? Which fertilizer should be used to get larger tomatoes? Which style of dress should our company manufacture (i.e., which style will lead to greater sales)?

My wife often asks me what appears to be a very similar question, “which dress do you think I should wear to the party?” But this question is really quite different from the others as it asks what a specific individual, me, thinks about dresses that are to be worn by another specific individual, my wife. All the other questions reference the behavior of a yet-to-be-determined individual selected at random from a population.

Is Alice taller than Peter? It won’t take us long to find out: We just need to put the two back to back or measure them separately.* The somewhat different question, “are girls taller than boys?” is not answered quite so readily. How old are the boys and girls? Generally, but not always, girls are taller than boys until they enter adolescence. Even then, ...