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41/9 FOP" i5» 19") will [titv'ﬁﬂfiﬁj J EEK/PEI". fig: V53“ 14 Expectation
0 Let X be a random variable, either dieorete or continuous, with known pmf or pdf.
The expected value, average? or mean is denoted by E [X] = {i a Let X be ediscrete random variable With pmf ELX] :o:Z:rP(X:'J:)
:rEX
and E [X] need not be arealizoble value of X a Example: A certain gas station has six pumps. Let X denote the number of pumps
that are in use at a particular time of day. The prob ability distribution is; below. What is the average number of pumps in use? /‘“\ 2 5p] .= am He!) MSW  ~ $603233 0 Let X be a continuous random variable with pdf '00 E'iX] : n : / mom —0() 0 Example: Let X denote the amount of time (in hours) for which a. book on 2~hour
reserve at a college library is checked out, Suppose that X has a probabiligéy distribution
given bdrm. 1 f T ﬁst) : ”gle e {0,21) ‘What is the average amount of timed book is checked out? I q "n“ I r
{’1’2 ,I gir «i, «g 3‘" f .3 (if :22
DE [AJTX XI 5 m ’3 )5 do :2 ”f 3 W; x 'r .
l t l all ”I L or
JG 2 27 1:. ___,. g 'r. (if:
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‘4' :3 0 Reed: Section 3.2
 Problems in Section 3.2: 32, 3.51 3.10 32 ...
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 Fall '07
 Carlton

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