A reminder that Exam #3 is available in Files, and is a take-home exam due Monday night (May 18). Here is an outline that may help you approach the exercises on the exam:
- #1: parts (a) and (b) are combinations calculations; you should write out these calculations in detail (see for example the solutions to HW8). Part (c) is a probability calculation which uses the results from (a) and (b), and (d) uses the result from (c). (The probability experiment in this exercise is randomly choosing 3 children from the class of 10 children; in (c) and (d) you are calculating the probabilities of the given events for this probability experiment.)
- #2: for part (a) compute the relative frequencies, and in part (b) graph them as a histogram. Part (c) involves calculating probabilities, assuming we interpret the relative frequencies as probabilities; see HW9-RandomVariables: Problem 2 for a similar example.
- #3: This is all about a binomial experiment/random variable, so review the class outline on that topic. In particular, review the definition of a binomial experiment, and refer to it to write out the explanation for part (b). For the table in part (c), it may help to review the Google spreadsheet we set up in class yesterday (Binomial Distribution Calculation), and to set up a similar one to help you fill out the table. For part (d), use the formulas that are given right there on the exam!
- #4: Parts (a) and (b) are similar to some of the exercises on HW9-RandomVariables (see Problems 2, 3, 5, 6). For part (c), use the definition of expected value E[X] which we covered on the class outline, and was also on Exam #2 (#2(b)).
- #5: For (b), again refer to the definition of a binomial experiment for your explanation (as in #3(b)); and for (c), use the formula for expected value of a binomial random variable (as given in #3(d)!). For (d), again refer to the Binomial Distribution Calculation spreadsheet we set up in class.
- But note that, as I said on the exam, you can just use the spreadsheet command =binomdist(i,n,p,false) to generate the binomial probability distribution of X, i.e., you don’t need to implement the entire binomial distribution formula, as we did in the shared spreadsheet.
- As with Exam #2, please submit the link to your spreadsheet for #5(d) along with your written solutions for the exam.
