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# Section5Notes - SECTION NOTE 5 ORIE360/560 FALL 2004 CHONG...

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SECTION NOTE 5 ORIE360/560, FALL 2004 CHONG WANG 1. Expected Values Expectation is one of the most important concepts in probability theory. Deﬁnition: For a discrete random variable X with a pmf p X , the expected value is deﬁned by E [ X ] = X x xp X ( x ) . For a continuous radom variable X with a pdf f X , the expected value is deﬁned by E [ X ] = Z -∞ xf X ( x ) dx. Example :(Problem 25, Chapter 4) A total of 4 buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40,33,25, and 50 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. (a) Which of EX or EY do you think is larger? Why? (b) Compute EX and EY . Solution : (a) EX is larger. The reason is for Y , no matter how many passengers on the bus, the four buses will be chosen with the same chances. But for X , the more passengers on the bus, the bigger chance the bus will get chosen. So relatively large values of

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Section5Notes - SECTION NOTE 5 ORIE360/560 FALL 2004 CHONG...

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