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5 note that x does not have to be a value that x can

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Unformatted text preview: random variable X(e) = age(e) + gpa(e) for each e in S. Here the "experiment" could just be picking a person e (and recording their name and age and gpa, say). Here not only age+gpa but also age and gpa individually are random variables, but name is not.  ­ Example: toss two fair coins and record which elem event (HH, HT, TH, or TT) occurs as above. Let X= ­2 if no Ts, +2 if equal number of T's and H's, and +4 if 2 Ts. (That is, let a T "count" as +2 and and H as  ­1). Then X is a random variable.  ­ Expected value (aka mean value, aka expectation) of a random variable. Definition: Given a sample space S, a prob dist P, and a random var X, we define E[X]=<X> = Sum_x_in_R [x P(X=x)] where P(X=x) means the prob of the event {e|X(e)=x}  ­ Example: the two ­coins just above. Then <X> =  ­2 P(X= ­2) + 2 P(X=2) + 4 P(X=4) =  ­2 (1/4) + 2(2/4) + 4 (1/4) =  ­1/2 + 1 + 1 = 1.5 Note that <X> does not have to be a value that X can actually have. It is essentially the notion of average value; e.g.,...
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