My account Contact me

CEGEP • Montreal

Probability and Statistics, 201-SN1-RE

Probability and Statistics, 201-SN1-RE, is the fourth mandatory mathematics course of the revised Sciences de la nature program, and a new one. It changes the question: no longer the exact value of a quantity, but what a sample allows you to claim about a population, and with what confidence. Every chapter has its corrected set and its revision sheet, from descriptive statistics to the chi-square test of independence.

8 fully corrected exercise sets (99 exercises), 8 revision sheets, and a practice paper. Free, no account needed. The same course in French.

Descriptive statistics

  1. 1 Descriptive statistics Population and sample, types of variables, tabulated data and data grouped into classes, mean, median and mode, variance and standard deviation, z-scores, percentile ranks, quartiles and box plots, on natural science data: fine particles, river flow, trout, ice, nitrates, precipitation. With the proofs of the course: the computing formula, the mean that minimizes the squared deviations, the divisor n minus 1. Sheet

Probability and random variables

  1. 2 Counting Choosing between permutation, arrangement and combination in one sentence, counting at least one through the complement, counting overlapping sets by inclusion-exclusion, reading a coefficient of the binomial theorem and proving Pascal's identity by counting spin configurations. Then science problems: DNA sequences and codons, a screening plan for additives on microplates, and two fictitious lotteries compared. Sheet
  2. 3 Probability and conditional probability From the axioms to the rules of calculation, proved. Mutually exclusive versus independent, contingency table, probability tree, law of total probability and Bayes' theorem proved, on natural science data: Mendelian genetics, environmental DNA, contaminated wells, a muon telescope, the reliability of a remote station. Then Monty Hall depending on what the person opening knows, and a drinking water test taken all the way to the decision. Sheet
  3. 4 Discrete and continuous random variables The distribution of a discrete variable and its step-shaped cumulative distribution function, expected value and variance, with the properties of E(aX+b) and V(aX+b) proved. Then the continuous variable with integral calculus: density and normalizing constant, probability by integration, cumulative distribution function, median, expected value and variance by substitution and by parts, the uniform distribution proved. Field data throughout: tree swallow nests, mutations, hailstones, germination, a lake echo sounder, seed dispersal. Sheet
  4. 5 Binomial and normal distributions Recognize a binomial distribution and see its conditions fail, prove E(X) = np and V(X) = np(1 - p), study the normal density and read its table both ways, standardize by a substitution, approximate a binomial by a normal with the continuity correction. Natural science contexts: germination, pH of rain, honeybee wings, powdery mildew, bacterial colonies. Sheet

Statistical inference

  1. 6 Confidence intervals: mean, Student's t and proportion The mean of a sample as a random variable, with its expected value and variance proved, the central limit theorem and its conditions, then the three intervals of the course: mean of a large sample, mean of a small sample with Student's t distribution, proportion. Sample size for a target margin, twenty simulated intervals to understand what 95% means, and two field studies: mercury in the walleyes of a lake and the size of a Canada goose population at a stopover site. Sheet
  2. 7 Hypothesis tests State H0 and H1 for seven natural science studies, then carry out the three tests of the course: a mean with a large sample (a fertilizer), a mean with Student's t distribution (the phosphorus of a lake, a flowering period), a proportion (malformed frogs). Critical region, p-value, the link with the confidence interval proved, Type I and Type II errors quantified on lead in drinking water, and the Student table recovered from an integral. Sheet

Relationship between two variables

  1. 8 Linear regression and the chi-square test of independence The relationship between two variables, on natural science data: scatter plot, covariance, correlation coefficient, least-squares line proved, coefficient of determination, interpolation and extrapolation, influential point and residuals. Then qualitative variables: contingency table, expected counts, degrees of freedom and the chi-square test of independence, up to a complete study of the salamanders of a forest. Sheet

When the chapters are done

A full paper under exam conditions. Do it once the chapters it covers are behind you: it measures what you can do on a question you have never seen.

Practice exam

Practice final exam, 201-SN1-RE

A three-hour final exam, eleven exercises marked out of 100, modelled on the course specification of the Science program's probability and statistics course: grouped data from a forest inventory, camera traps and Bayes' theorem, pooled testing, the density of burned areas, salmon smolts and the binomial distribution, radon and a test on a mean, Student's t distribution on a spring, ticks and a proportion, regression of dissolved oxygen, and a complete problem on road salt and wood frogs.

  • 11 questions
  • 100 points
  • 180 minutes
Sit the paper

What you need beforehand

201-SN1-RE relies on 3 chapters from earlier courses. These are not comfort revisions: each one supports a chapter listed above, and a student who falls behind during the year almost always falls behind on one of them. Each one has its revision sheet, to read in one sitting before the term starts. 2 of them are written in French, like the Quebec secondary program they come from.

Secondary 3

Secondary 4

201-SN3-RE

Need support and not only exercises? CEGEP tutoring in Montreal

Looking for a tutor in Montreal?

Get in touch for a first session. We work on exercises set at the real level of your CEGEP's exams, in English or in French.

Contact me WhatsApp
Site by Studio Squalli