An environmental engineer working for the EPA is tasked with observing water spec- imens from lakes in northeast Georgia. In this region, each water specimen has a 10 percent chance of containing a particular organic pollutant.
(a) Treating each water specimen as a “trial,” suppose the three Bernoulli trial assump- tions hold. State what this would imply (i.e., just give the assumptions for this situation). (b) Let Y denote the number of specimens that contain the pollutant out of the next 15 analyzed. Plot the pmf and cdf of Y side by side . Place an “×” on the pmf indicating where E(Y ) is.
(c) In part (b), find the probability that • there is exactly 1 polluted sample
• there are 3 or more polluted samples (this event will trigger an EPA intervention). Note: For practice, I want you to do part (c) “by hand,” that is, show all the calculations
with pencil and paper. Use R to check your work.
(d) In part (b), if the engineer found 10 or more of the 15 specimens to be polluted, what might be true?