1.6 lecture06

1.6 lecture06 - 1 STAT 1301 Probability &...

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Unformatted text preview: 1 STAT 1301 Probability & Statistics Lecture 6 Random Variables • In most problems we are interested only in a particular aspect of the outcomes of experiments. • Example: When we toss 10 coins, we are interested in the total number of heads, and not the outcome for each coin. • For a given sample space S , a random variable (rv) is a real-valued function defined over the elements of S . • A random variable reflects the aspect of a random experiment that is of interest to us. • There are two types of random variables – A discrete random variable has at most a Random Variables A discrete random variable has at most a countable number of possible values. – A continuous random variable takes all values in an interval of numbers. • The probability distribution of a r.v. X tells us what the possible values of X are and how probabilities are assigned to those values. • Experiment: A fair die is thrown twice. • Let X be the average number of spots showing on two throws. Example Outcome X Outcome X Outcome X 1 1,1 1 13 3,1 2 25 5,1 3 2 1 2 1 5 1 3 2 2 5 26 5 2 3 5 2 1,2 1.5 14 3,2 2.5 26 5,2 3.5 3 1,3 2 15 3,3 3 27 5,3 4 4 1,4 2.5 16 3,4 3.5 28 5,4 4.5 5 1,5 3 17 3,5 4 29 5,5 5 6 1,6 3.5 18 3,6 4.5 30 5,6 5.5 7 2,1 1.5 19 4,1 2.5 31 6,1 3.5 8 2,2 2 20 4,2 3 32 6,2 4 9 2,3 2.5 21 4,3 3.5 33 6,3 4.5 10 2,4 3 22 4,4 4 34 6,4 5 11 2,5 3.5 23 4,5 4.5 35 6,5 5.5 12 2,6 4 24 4,6 5 36 6,6 6 Outcome X Outcome X Outcome X 1 1,1 1 13 3,1 2 25 5,1 3 2 1,2 1.5 14 3,2 2.5 26 5,2 3.5 3 1,3...
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1.6 lecture06 - 1 STAT 1301 Probability &...

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