Chapter 2.1 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Definition of probability

# Chapter 2.1 - Math3200 Intermediate Probability and...

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Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

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Definition of probability Classical Equally possible outcomes Frequentist Long term relative frequency Subjective A personal assessment of the chance that a given outcome will occur Can be applied to one-time phenomena that are not repeatable Vary from person to person
Sample space and events Random experiment A procedure whose outcome is uncertain and can not be predicted in advance Sample space (S) The collection of all possible outcomes of a random experiment Discrete vs. continuous Event A set of outcomes of a random experiment A subset of the sample space S

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Event algebra Union: A or B Intersection: A and B Complement: not A Disjoint events A and B have no outcomes in common Venn diagram
Operations on Sets Complement Intersection Union

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A Business Problem In reviewing the portfolio of 365 of its clients, a mutual funds company categorized whether the clients were invested in international stock funds, domestic stock funds, or bond funds. It found that, 125 were invested in domestic stocks, international stocks, and bond funds; 145 were invested in domestic stocks, and bond funds; 300 were invested in domestic stocks; 200 were invested in domestic stocks and international stocks; 18 were invested in international stocks and bond funds, but not domestic stocks; 35 were invested in bond funds, but not domestic stocks or international stocks ; 87 were invested in international stocks, but not bond funds ;
a) How many were invested in international stocks? b) How many were invested in bonds, but not international stocks c) How many were not invested in bonds? d) How many were invested in international or domestic stocks?

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I D B 125 20 75 80 18 35 12 a) How many were invested in international stocks? 12+18+125+75=230 b) How many were invested in bonds, but not international stocks 35+20=55 c) How many were not invested in bonds? 12+75+80=167 d) How many were invested in international or domestic stocks? 365-35=330