** T**his year is my daughter’s final year in high school and she is now taking the dreaded baccalauréat exams. Just like a few hundred thousands French students. With “just like” in the strict sense since all students with the same major take the very same exam all over France… The first written composition is in the “mother of all disciplines”, philosophy, and the theme of one dissertation this year was *“do we live to be happy?”*. Which suited well my daughter as she was hoping for a question around that theme. She managed to quote Plato and Buddha, The Pursuit of Happiness and The Wolf of Wall-street… So sounded happy enough with her essay. This seemed indeed like a rather safe notion (as opposed to ethics, religion, politics or work), with enough material to fill a classical thesis-antithesis-synthesis plan (and my personal materialistic conclusion about the lack of predetermination in our lifes).

## Archive for exam

## Vivons-nous pour être heureux ? [bacc. 2014]

Posted in Books, Kids with tags Baccalauréat, essay, exam, France, happiness, philosophy on June 20, 2014 by xi'an## Bayes at the Bac’ [again]

Posted in Kids, Statistics with tags Baccalauréat, Cartesian geometry, complex numbers, exam, high school, integrals, polynomials, sequence, Thomas Bayes on June 19, 2014 by xi'an**W**hen my son took the mathematics exam of the baccalauréat a few years ago, the probability problem was a straightforward application of Bayes’ theorem. (Problem which was later cancelled due to a minor leak…) Surprise, surprise, Bayes is back this year for my daughter’s exam. Once again, the topic is a pharmaceutical lab with a test, test with different positive rates on two populations (healthy vs. sick), and the very basic question is to derive the probability that a person is sick given the test is positive. Then a (predictable) application of the CLT-based confidence interval on a binomial proportion. And the derivation of a normal confidence interval, once again compounded by a CLT-based confidence interval on a binomial proportion… Fairly straightforward with no combinatoric difficulty.

**T**he other problems were on (a) a sequence defined by the integral

(b) solving the equation

in the complex plane and (c) Cartesian 2-D and 3-D geometry, again avoiding abstruse geometric questions… A rather conventional exam from my biased perspective.

## ultimate R recursion

Posted in Books, R, Statistics, University life with tags accept-reject algorithm, computer language, exam, Monte Carlo methods, normalising constant, R, recursion on January 31, 2012 by xi'an**O**ne of my students wrote the following code for his R exam, trying to do accept-reject simulation (of a Rayleigh distribution) and constant approximation at the same time:

fAR1=function(n){ u=runif(n) x=rexp(n) f=(C*(x)*exp(-2*x^2/3)) g=dexp(n,1) test=(u<f/(3*g)) y=x[test] p=length(y)/n #acceptance probability M=1/p C=M/3 hist(y,20,freq=FALSE) return(x) }

which I find remarkable if alas doomed to fail! I wonder if there exists a (real as opposed to fantasy) computer language where you could introduce constants C and only define them later… (What’s rather sad is that I keep insisting on the fact that accept-reject does not need the constant C to operate. And that I found the same mistake in several of the students’ code. There is a further mistake in the above code when defining *g*. I also wonder where the *3* came from…)

## R exam

Posted in Kids, pictures, Statistics, University life with tags exam, harmonic mean estimator, Introduction to Monte Carlo Methods with R, Méthodes de Monte-Carlo avec R, Monte Carlo methods, R, simulation, Université Paris Dauphine on November 28, 2011 by xi'an**F**ollowing a long tradition (!) of changing the *modus vivendi* of each exam in our exploratory statistics with R class, we decided this year to give the students a large collection of exercises prior to the exam and to pick five among them to the exam, the students having to solve two and only two of them. (The exercises are available in French on my webpage.) This worked beyond our expectations in that the overwhelming majority of students went over all the exercises and did really (too) well at the exam! Next year, we will hopefully increase the collection of exercises and also prohibit written notes during the exam (to avoid a possible division of labour among the students).

**I**ncidentally, we found a few (true) gems in the solutions, incl. an harmonic mean resolution of the approximation of the integral

since some students generated from the distribution with density *f* proportional to the integrand over [2,∞) [a truncated gamma] and then took the estimator

although we expected them to simulate directly from the exponential and average the sample to the fourth power… In this specific situation, the (dreaded) harmonic mean estimator has a finite variance! To wit;

> y=rgamma(shape=5,n=10^5) > pgamma(2,5,low=FALSE)*gamma(5) [1] 22.73633 > integrate(f=function(x){x^4*exp(-x)},2,Inf) 22.73633 with absolute error < 0.0017 > pgamma(2,1,low=FALSE)/mean(y[y>2]^{-4}) [1] 22.92461 > z=rgamma(shape=1,n=10^5) > mean((z>2)*z^4) [1] 23.92876

**S**o the harmonic means does better than the regular Monte Carlo estimate in this case!

## R [re-]exam

Posted in Books, R, Statistics, University life with tags exam, graduate course, I love R, plagiarism, R on March 28, 2011 by xi'an**I**n what seems like an endless cuRse, I found this week I had to re-grade a dozen R exams a TA’s did not grade properly! The grades I (X) got are plotted below against those of my TA (Y). There is little connection between both gradings… As if this was not enough trouble, I also found exactly duplicated R codes in another R project around ** Introducing Monte Carlo methods with R** that was returned a few weeks ago. Meaning I will have to draft a second round exam… (As Tom commented on an earlier post, team resolution of a given problem may be a positive attitude, but in the current case one student provided an A⁺⁺ answer, while two others clearly drafted an hasty resolution from the original.) Nonetheless, do not worry, I still love [teaching] R!