ts, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random permutation. We denote by a the integer formed in base 10 by the first five positions in this permutation and by b the integer formed in base 10 by the last five positions in this permutation (either a or b may begin with 0 which in such a case is ignored). For example, if the random permutation is 8621705394 then a = 86217 and b = 5394. Consider the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product ab is even and X = 0 when that product is odd. Calculate E[X].
ts, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random permutation. We denote by a the integer formed in base 10 by the first five positions in this permutation and by b the integer formed in base 10 by the last five positions in this permutation (either a or b may begin with 0 which in such a case is ignored). For example, if the random permutation is 8621705394 then a = 86217 and b = 5394. Consider the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product ab is even and X = 0 when that product is odd. Calculate E[X].
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 54SE: How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and...
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The 10 decimal digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random permutation. We denote by a the integer formed in base 10 by the first five positions in this permutation and by b the integer formed in base 10 by the last five positions in this permutation (either a or b may begin with 0 which in such a case is ignored). For example, if the random permutation is 8621705394 then a = 86217 and b = 5394. Consider the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product ab is even and X = 0 when that product is odd. Calculate E[X].
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