Stat400Lec5(Ch2.1_2.3)_ans - St&t 400 lecture 5...

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Review(Chapter 1) e Experiment, events, set theoretic terminology o Probability rules, Bayes's theorem o lndependence * o Method of enumeration Today's leaure(2.1., 2.2, 2.3) o Random variable, space. o Discrete random variable, probability mass function and its properties. r Uniform distribution, Hypergeometric distribution r Mathematical expectation (mean,variance,standard de- viation, moment) e Properties of mathematical expectation (mean,variance) Stat 400 tEcturc 5 Spriu 2012 Example: Wheel of fortune. One spins a wheel and look at the angle of the pointer. lf the angle is within [0',180'), then one gets 1000 dollars, otherwise he/she gets 0 dollars. Let X be the dollar amount the person gets. r What is the outcome space ? I o', ][,o') o What is the space for X ? $= [ X= g o( loro] o ls X a discrete random variable? \/ let Probability mass function The probability mass function (p.r.f.) /(r), for a dis- crete random variable X, is given by f(r):P(X:r), r€S Example: Paul rolls a defect dice with numbers 1,2,3,3,3,3 on six faces. Which number? r ltzl 7r)]"-r-TT ifr:1 i{r:2 ifr:3 otherwise St&t 400 leture 5 Spriry 2012 Random variable Definition: Given a random experiment with an outcome space S, a function X that assigns to each element s in S one and only one real number X(s) : r is called a random uariable. The random variable X is discrete if the set of real values it can take if finite or countable, e.g. {0, 1,2, 3, . . . , }. Example: Paul rolls a defect dice with numbers 1,2,3,3,3,3 on six faces. Random experiment: which number? Random variable: X gives numbers to the possible out- comes. Definition: The space (support) of X is the set of real numbers {r : X(s) : o, s € ,S}. ln the book, the space of X is denoted by S, same as sample space. rSpaceofX:S:
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Stat400Lec5(Ch2.1_2.3)_ans - St&t 400 lecture 5...

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