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a define the expected value of a random variable xb what is the expected value of the random variable x that assigns to
in 2010 the puzzle designer gary foshee posed this problem mr smith has two children one of whom is a son born on a
use chebyshevs inequality to show that the probability that more than 10 people get the correct hat back when a
suppose that n balls are tossed into b bins so that each ball is equally likely to fall into any of the bins and that
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there are three cards in a box both sides of one card are black both sides of one card are red and the third card has
suppose that a fair octahedral die and a fair dodecahedral die are rolled togethera what is the expected value of the
given a positive integer n simulate n repeated flips of a biased coin with probability p of heads and determine the
given positive integers n and m generate m random permutations of the first n positive integers sort each permutation
given positive integers m and n simulate the placement of n keys where a record with key k is placed at location hk k
given a positive integer n find the probability of selecting the six integers from the set 1 2n that were mechanically
given a list of words and the empirical probabilities they occur in spam e-mails and in e-mails that are not spam
estimate the probability that two integers selected at random are relatively prime by testing a large number of
given positive integers m and n generate m random permutations of the first n positive integers find the number of
the following two sentences were devised by the logician saul kripke while not intrinsically paradoxical they could be
as strange as it may seem it is possible to give a precise looking verbal definition of an integer that in fact is not
indicate whether the statements in parts a-d are true or false justify your answersa if two elements in the domain of a
in let x and y be sets let a and b be any subsets of x and let c and d be any subsets of y determine which of the
in indicate which of the functions in the referenced exercise are one-to-one correspondences for each function that is
in s denotes the set of real numbers strictly between 0 and 1 that is s x isin r 0define a function g from the set of
use the technique illustrated in example 854 to find all possible solutions for the problemsa gym purchased 2-pound
use the technique illustrated in example 854 to find one particular solution and the formulas for the general solutions
cross rates use the foreign exchange section of a current issue ofthe wall street journalto look up the three
a find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one
a find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0sb what are