A payoff, a P&L, a default count, a number of trade fills — none of these are "events" in the abstract sense of Probability Foundations; they are numbers that depend on chance. A random variable is the object that formalises "a number that depends on the outcome of an experiment," and this topic builds its complete elementary toolkit for the discrete case: the probability mass function that assigns probability to each possible value, expectation and variance as the number's average value and spread, the machinery for handling functions of a random variable, joint PMFs for several random variables at once, and conditioning and independence restated for random variables rather than bare events. The topic closes with a derivation sub-note carrying the algebra for the four named discrete distributions' moments.
By the end of this topic you should be able to:
- define a discrete random variable's PMF from a probabilistic model, and compute it for the four standard named distributions (Bernoulli, Binomial, Geometric, Poisson);
- compute the expectation and variance of a discrete random variable directly from its PMF;
- apply the expected value rule (LOTUS) to compute without first finding 's own PMF;
- construct and read a joint PMF for two random variables, extract marginals, and compute conditional PMFs;
- test two random variables for independence, and derive the mean/variance of the named distributions from first principles.
In this lesson
- Contents
- The big picture
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