Page 34 - FINAL CFA I SLIDES JUNE 2019 DAY 3

LOS 10.a: Define a probability distribution and Session Unit 3:
distinguish between discrete and continuous random
variables and their probability functions, p214. 10. Common Probability Distributions

LOS 10.b: Describe the set of possible outcomes of a specified discrete random variable.

A probability distribution (function) (PF) describes the p of all the possible outcomes for a RV with a sum of 1 (e.g. roll of a fair
die 1/6, 1/6, 1/6…1/6 = 1).

Check: p(x), or P (X = x) i.e. P that RV X takes on the value x. or p. X = 2 on die is 1/6!

DRV -no. of outcomes can be counted with a measurable and +ve probability (no. sides in fair die) and for a CRV, the no.
outcomes is infinite, even if lower and upper bounds exist (e.g. continuous compounding (ex)? or rainfall in inches, half
inches, quarter inches, etc., share price – seems discrete but in practice, treated as continuous?

For a DD, p(x) = 0 -x cannot occur, or p(x) > 0 if it can e.g. calendar month: 33/30 vs 25/30?;

For a CD, p(x) = 0 even though x can occur (lower and upper bounds: P(x1 ≤ X ≤ x2), e.g. probability share price will
change is often a range than point estimate!