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18.05 | Spring 2014 | Undergraduate

# Introduction to Probability and Statistics

### Reading Questions Answer Checker

To check your answers put them in the appropriate box and click the ‘Check’ button. Every checker box can do arithmetic and calculate standard functions (see calculator help). If you give decimal answers, give them to at least 3 decimal places.

As you work you should have pencil and paper handy for calculations and thinking!

Note: some questions ask for a formula. For the checker we ask you to plug a value into the formula. For your pset you still need to give the whole formula.

//DEBUG PARAMETERS //Because we don’t show solutions for pset checkers we use //this to give a showanswer button during the debugging phase var debugans = undefined; //release //var debugans = kDebugAnswer; //debug problemNumber = 0; wl("<h3>Calculator</h3>"); writecalculator(“psetcheckcalcid”, “Calculate”); whr(kdivcol,kdivwid);

//Problem 1 problemNumber++; wl(problemheader(problemNumber)); var s; var partName, problemName, buttonLabel, answerArray, correct; s = [“Recall the coin example from the reading:”, kbr, “There are three types of coins which are indistinguishable apart from their probability of landing heads when tossed.”, kp, “<ul>”, “<li>Type $A$ coins are fair, with probability .5 of heads</li>”, “<li>Type $B$ coins have probability .6 of heads</li>”, “<li>Type $C$ coins have probability .9 of heads</li>”, “</ul>”, kp, “You have a drawer containing 4 coins: 2 of type $A$, 1 of type $B$, and 1 of type $C$. You reach into the drawer and pick a coin at random.”, kp, “Suppose you toss the coin 5 times and it lands tails all 5 times. What are the posterior probabilities? Hint: do the updating in one go.”, kp, “Give your answers to 3 decimal places.”]; wl(s.join(’ ‘)); wl(kp); s = “$P(A|D)$”; wl(s); wl(kp); partName = problemNumber + " (i)"; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 0.85911, buttonLabel, 0.005, kuseCorrectVal); wl(kp); s = “$P(B|D)$”; wl(s); wl(kp); partName = problemNumber + " (ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, .14076, buttonLabel, 0.005, kuseCorrectVal); wl(kp); s = “$P(C|D)$”; wl(s); wl(kp); partName = problemNumber + " (iii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 0.000137, buttonLabel, 0.001, kuseCorrectVal); wl(kp); whr(kdivcol,kdivwid);

//Problem 2 problemNumber++; wl(problemheader(problemNumber)); var s; var partName, problemName, buttonLabel, answerArray, correct; s = [”<b>Stubborn priors.</b> Suppose you run an experiment to test 3 different hypotheses: $A$, $B$, and $C$. You are so convinced that $B$ is the correct hypothesis that your prior is", kp, “$P(A) = 0$,” + ksp + ksp + “$P(B) = 1$,” + ksp + ksp + “$P(C) = 0.$”, kp, “You collect data $D$ with likelihoods”, kp, “$P(D|A) = 0.8,$” + ksp+ksp +"$P(D|B) = 0.01$," +ksp +ksp + “$P(D|C) = 0.7$”]; wl(s.join(’ ‘)); wl(kp) s = “(a) Compute the posterior probabilities:”; wl(s); wl(kp); s = “$P(A|D)$”; wl(s); wl(kp); partName = problemNumber + " (a.1)"; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 0.0, buttonLabel, 0.0001, kuseCorrectVal); wl(kp); s = “$P(B|D)$”; wl(s); wl(kp); partName = problemNumber + " (a.2)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 1.0, buttonLabel, 0.0001, kuseCorrectVal); wl(kp); s = “$P(C|D)$”; wl(s); wl(kp); partName = problemNumber + " (a.3)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 0.0, buttonLabel, 0.0001, kuseCorrectVal); wl(kp); s = “(b) Will any amount of data change your belief that $B$ is the correct hypothesis?” wl(s); wl(kbr); partName = problemNumber + " (b)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; correct = “No”; var answerArray = [“Yes”, correct]; writeMultipleChoiceRadioGroup(answerArray, problemName, correct, buttonLabel); wl(kp); whr(kdivcol,kdivwid);

## Course Info

##### Instructors

- Dr. Jeremy Orloff
- Jonathan Bloom

##### Departments

- Mathematics

##### As Taught In

Spring 2014

##### Level

Undergraduate

##### Topics

- Mathematics
  - Discrete Mathematics
  - Probability and Statistics

##### Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes
co_present Instructor Insights
theaters Other Video

Browse Resources

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