expected value and variance

# expected value and variance - Expected Value and...

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Expected Value and Variance *Classic Probability asserts that the expected value of a random variable is the long-run average value of the random variable in independent observations. The expected value of a discrete random variable X, denoted E[X], is defined by Expected value E[X]= x X x p x ) ( * In words, the expected value of a discrete random variable is a weighted average of its possible values, and the weight used is its probability. Sometimes, the expected value is referred to as the expectation, the mean, or the first moment. Also, sometimes it is denoted as X µ . For a function of x g(x), we have the following: E[g(X)]= ()* () X x gx p x . So, if we define g(x) = 2 x , we have E[ 2 x ] = 2 * () X x x px . Siblings (x) Probability ) ( x p X X* ) ( x p X 0 .200 .000 1 .425 .425 2 .275 .550 3 .075 .225 4 .025 .100 1.000 1.300 As we can see, the expected value of our sibling example is 1.3. This implies that if we randomly select a student then the expected number of siblings they have is 1.3.

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Clearly a student can’t have 1.3 siblings. However, if we continue to select students at random, the average number of siblings we obtain will be close to 1.3.
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## This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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expected value and variance - Expected Value and...

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