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Unformatted text preview: Statistics 21, Distribution Table, Expected Value, and SE 1) A random variable is a quantity determined by the outcome of an experiment of some sort. N and X are random variables in the examples. a) N = the number of spots appearing on a die roll. b) X = the number of times a six appears in two die rolls. 2) A distribution table is a table which displays the possible values of a random variable and their probabilities. Note that all the probabilities must add up to 1. Continuing examples a) and b) from above: n 1 2 3 4 5 6 P( N = n ) 1 6 1 6 1 6 1 6 1 6 1 6 x 1 2 P( X = x ) 25 36 10 36 1 36 3) The expected value of a random variable is defined to be the sum of the products x P( X = x ). The sum is taken over all possible values of X in the distribution table and is typically written: E( X ) = summationdisplay x x P( X = x ) a) For the number of spots appearing on a die roll, the expected value is: summationdisplay n n P( N = n ) = 1 1 6 + 2 1 6 + 3 1 6 + 4 1 6 + 5 1 6...
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