This course provides an introduction to probability using simulation and mathematical frameworks with emphasis on the probability concepts needed for more advanced study in statistical practice.
Topics covered include
- probability spaces and random variables;
- discrete and continuous probability distributions;
- probability mass, density, and distribution functions;
- expectations and variance;
- independence and conditional probability; and
- the law of large numbers, the central limit theorem, and sampling distributions.
What is probability? Consider the Monty Hall Dilemma example from the textbook (Dekking et al. 2005, sec. 1.3, p. 4). You are asked the following question:
Suppose you’re on a game show, and you’re given the choice of three doors; behind one door is a car; behind the others, goats.
Example: Two Dice, Two Random Variables Adopted from Dekking et al. (2005) Section 9.1.
Suppose you roll two six-sided, fair dice. Let \(S\) be the sum of the two rolls and \(M\) be the maximum of the two rolls.
Example: Labour Force Survey (From StatCan website: https://www.statcan.gc.ca/eng/survey/household/3701)
The Labour Force Survey (LFS) is a household survey carried out monthly by Statistics Canada. It is the only source of current, monthly estimates of total employment and unemployment…The survey is conducted in 54,000 households across Canada…to determine the characteristics of an entire population by using the answers of a much smaller, randomly chosen sample…