Final Exam: Guide to Written Solutions


For the final exam, you should complete 10 exercises in the “Final Exam Exercises” WebWork set, and also submit the following written solutions and spreadsheet calculations.

The WebWork exercises and your written solutions (& spreadsheet link) are due Friday at 5pm. Good luck!

#1: Write down your calculation for “The percentage of students with over X dollars in their possession” (in terms of the frequencies shown on the histogram and the sample size n).

#2: Calculate the regression parameters in a spreadsheet. Write out the calculation of the predicted value in your written solutions.

#3: Write out each probability as a ratio of two integers, and use the “P(event)” notation.

#4: For each of the probabilities you are asked for, write down the set of outcomes in the event.

#5: Write down P(A), P(B), and P(A and B) (using the given information), and then write out the calculations of  conditional probabilities asked for in the exercise (using the definition of conditional probability).

#6: Write down the calculation of the size of the sample space for this probability experiment (of choosing a committee of four at random from this group of people).  Then write down the calculations of the following probabilities: (a) the committee consists of all women, and (b) the committee contains at least one man. (Hint: See Exam #3, Exercise #1.)

#7: Write down the probability distribution for the random variable X = “your net win/loss in this raffle” and write out your calculation of the expected value E[X].  (Note: WebWork requires you to include “$” in your typed solution for this exercise, and if you find the expected value is negative, include a negative sign before the dollar sign. For example, to enter an expected value of negative 50 cents, enter “-$0.50”)

#8: Write out the calculation of the expected value.

#9: Write down the values of n, p, and q for this binomial experiment.  Write down the calculations of the expected value and standard deviation. (Hint: use the formulas given on the class outline and on Exam #3.)

Calculate the entire binomial probability distribution for this binomial random variable in your spreadsheet (using the spreadsheet function =binomdist(i, n, p, false)).  Use  your spreadsheet to calculate the probability asked for in the exercise.

#10: Sketch the normal distribution curve with the given mean and standard deviation (see the last class outline!). Indicate on your sketch the areas under the curve corresponding to the probabilities asked for in the exercise, using the notation “P(X < c)” or “P(X > c)” for each.

Finally, calculate the given probabilities in your spreadsheet (using the spreadsheet function “=normdist(c, mean, stddev, true” which outputs P(X < c)) .

You can ignore part (c) for this exercise!

Guide to Exam #3

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.

Notes on Mon May 11 Blackboard / Exam #3 / Final Exam schedule

See below for a list of topics we discussed during Monday’s Blackboard session. We also discussed the exam schedule:

  • Exam #3 will be a take-home exam (similar in format to Exam #2), which will be posted later today and will be due Monday (May 18)
    • Recall that the lowest of your three midterm exam scores will be dropped, i.e., your two highest midterm exam scores will be counted towards your course grade.
    • So if you are satisfied with your first two exam scores, you can skip handing in Exam #3. But I encourage you to at least attempt the exercises on Exam #3, since they will be good review for the final exam.
  • The final exam will be a set of WebWork exercises for which you will also submit written solutions.  The final exam exercises will be assigned next Wed (May 20), to be completed by Friday May 22.
    • There will be a set of 10 WebWork exercises for which you will submit answers online via WebWork
    • You will also need to submit written solutions for those WebWork exercises, so that I can check your work and allow the possibility of partial credit.
  • We will have Blackboard sessions today (Wed May 13) as well as next Monday (May 18) and Wednesday (May 20), to discuss the exams and go over some remaining new material.   Wednesday May 20 will be our last Blackboard session.
  • There will be no projects, so I will post a revised grading scheme: your course grade will be made up of your midterm exams, final exam, WebWork, quizzes, and participation (some additional ways of earning participation points will be posted this week.)

Topics discussed on Monday’s Blackboard session:

  • 0-60mins: went over Exam #2 solutions
  • 60-90mins: revisited class outline on binomial experiments, and discussed the binomial distribution formula
  • 90-125mins: set up example for computing a binomial probabilities in Google spreadsheet: Binomial Distribution Calculation

We will continue with that spreadsheet during today’s Blackboard session!  I will also discuss the exercises on Exam #3, so please join today’s Blackboard session.


Exam #2: Take-home exam due Sunday, May 3

Exam #2 is a take-home exam due Sunday; I have uploaded the pdf to Files. We also discussed some of the exam questions at the end of today’s Blackboard Collaborate class session.

As with the recent Quiz #3 and HW8, write out your solutions and submit them via Blackboard-Assignments, preferably as a single pdf file.

You will also need to submit a spreadsheet for the last exercise on the exam. As I wrote on the exam, you can either submit the spreadsheet as an additional attachment with your pdf, or you can copy/paste the share link as a comment when you submit your written solution.

Email me if you have any questions about the exam, or about related examples or exercises! I will have office hours Thursday and Friday via Blackboard Collaborate for questions (times TBA tomorrow morning).

Exercise: Probability Distribution (X = sum of two 6-sided dice)

We have previously discussed the probability experiment of rolling two 6-sided dice and its sample space.  Now we can look at random variables based on this probability experiment. A natural random variable to consider is:

X = sum of the two dice

You will construct the probability distribution of this random variable. For reference, I wrote out the sample space and set up the probability distribution of X; see the snapshot below.

It will be a exam exercise to complete the probability distribution (i.e., fill in the entries in the table below) and to graph the probability distribution (i.e., as a histogram):

Sample space of rolling two 6-sided dice

Exam #1 – Wed March 4

As I announced in class, we will take our first midterm exam this Wednesday (March 4).  The exam will cover the material up to and including basic probability.

Here is a list of concepts/topics that will be covered on the exam:

  • frequency tables, relative frequencies, frequency histograms
  • measures of central location: mean & median
  • measures of variability: sample standard deviation, sample variance
  • quartiles, 5-number summary, box plots
  • paired data sets: scatterplots, positive vs negative correlation, the correlation coefficient, linear regression
  • basic concepts of probability: simple probability experiments, sample spaces, events

Here is a guide on how to prepare for the exam:

  • do these exercises from “HW5-Probability”: #1, 2(a)-(d), 4, 5(a)-(c), 8, 9
  • review the outlines/notes/spreadsheets for Classes#1-8 (available under Files and the Calendar page)
  • review the solutions to Quiz 1 and Quiz 2 (available under Files)
  • review the WebWork exercises and solutions from “HW2-Graphs”, “HW3”, and “HW4-PairedData”
  • in particular, review the following WebWork exercises:
    • HW2-Graphs: #2, 3, 4, 10, 11, 13, 14
    • HW3: #1, 2, 3, 5, 10
    • HW4-PairedData: #1, 3, 6, 13, 14, 20, 21, 22

(Note that you can view solutions for past WebWork sets by clicking on “Download PDF or TeX Hardcopy for Current Set” and selecting the options for “Show: