**SLR 511F: 10 MATHEMATICAL IDEAS EVERYONE SHOULD KNOW and their everyday applications in the real world **

(John Clements. Thanks for taking the time to share some mathematical ideas with me in SESSION #1.

** Mon. Sept. 19 we will begin TOPIC #3 **

** TOPIC #3: The simplest ideas in probability and and statistics and the mathematics of finance: **

** (i) The basic ideas behind Probability Theory with examples **

** Random Processes => SAMPLE SPACE S (all possible outcomes - DRAW TREE DIAGRAM) **

** SAMPLE SPACE S = {s1,s2,...............,sn} **

** with probabilities Pr = {p1,p2,...............,pn} **

** Probabilities and their Properties: INDEPENDENT EVENTS MULTIPLY and MUTUALLY EXCUSIVE OUTCOMES ADD **

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** GIVEN NUMERICAL REWARDS X associated with the outcomes in the sample space S, X = { x1,.....,xk} **

** with probabilities = { f1,.....,fk} (from the {p1,p2,...............,pn}) **

** E(X) = EXPECTED VALUE of the rewards = x1*f1 +.............+ xk*fk **

** (ii) Statistics: mean, variance, standard deviation, etc., Surveys, etc.
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