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a certain town never has two sunny days in a row each day is classied as being either sunny cloudy but dry or rainy if
1 every time that the team wins a game it wins its next game with probability 08 every time it loses a game it wins its
each individual in a population of size n is in each period either active or inactive if an individual is active in a
consider the following approach to shufing a deck of n cards starting with any initial ordering of the cards one of the
each morning an individual leaves his house and goes for a run he is equally likely to leave either from his front or
in a good weather year the number of storms is poisson distributed with mean 1 in a bad year it is poisson distributed
suppose that coin 1 has probability 07 of coming up heads and coin 2 has probability 06 of coming up heads if the coin
1 three white and three black balls are distributed in two urns in such a way that each contains three balls we say
suppose the numbers of families that check into a hotel on succes- sive days are independent poisson random variables
suppose that a production process changes states in accordance with an irreducible positive recurrent markov chain
a pensioner receives 2 thousand dollars at the beginning of each month the amount of money he needs to spend during a
1 an urn always contains 2 balls ball colors are red and blue at each stage a ball is randomly chosen and then replaced
a gambling modelconsider a gambler who at each play of the game either wins 1 with probabilitynbsppnbspor loses 1 with
a markov chain whose state space is given by the integers i 0 plusmn1 plusmn2 is said to be a random walk if for some
1 an urn contains n white and m black balls that are removed one at a time if n gt m show that the probability that
1 consider a gambler who on each bet either wins 1 with probability 1838 or loses 1 with probability 2038 these are the
in a knockout tennis tournament of 2n contestants the players are paired and play a match the losers depart the
1 a coin having probability p of coming up heads is continually ipped let pjn denote the probability that a run of j
the opponents of soccer team a are of two types either they are a class 1 or a class 2 team the number of goals team a
1 at a partynbspnnbspmen take off their hats the hats are then mixed up and each man randomly selects one we say that a
suppose that we are to be presented with n distinct prizes in sequence after being presented with a prize we must
a miner is trapped in a mine containing three doors the rst door leads to a tunnel that takes him to safety after two
question 1shown below are rental and leasing revenue gures for ofce machinery and equipment in the united states over a
suppose that the expected number of accidents per week at an indus- trial plant is four suppose also that the numbers
1 sam will read either one chapter of his probability book or one chapter of his history book if the number of