COMP 1002 Unit 9 overview
In this unit we will talk about (finite) probability. In addition to basic concepts, we will cover conditional probability and Bayes theorem (commonly used in data science and in AI) as well as computing expected values such as expected number of tries to get a result, and estimating deviation from the mean, in particular using variance. We will look at random variables, and useful properties such as linearity of expectation.
Readings
Chapter 7.
Learning objectives
You will learn basic concepts of finite probability, and learn how to compute probabilities of various events. You will use Bayes theorem to solve problems, and determine expected value of various random variables, in particular expected time/number of steps until an event occurs. You will see how to estimate probability that the value of a random variable is far from the mean. Overall, you will be expected to know how to solve problems similar to ones in the lectures, lab, online exercises and the practice problem set.
Vocabulary
You need to know the meaning of the following terminology (and respective notation):
- Experiment, outcome, sample space, event, probability of an event.
- Probability distribution, uniform distribution, biased vs. fair coin/dice.
- Conditional probability of an event.
- Pairwise disjoint events, independent events, mutually independent events.
- Birthday paradox, Monty Hall puzzle, hat check puzzle
- Bayes theorem, sensitivity, specificity, true/false positives/negatives.
- Bernoulli trials.
- Random variable, and its expected value (expectation, mean). Indicator random variable.
- Variance and standard deviation of a random variable
- Markov's inequality and Chebyshev's inequality.
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