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question a card contains n chips and has an error-correcting mechanism such that the card still functions if a single
question suppose that a queue has n servers and that the length of time to complete a job is an exponential random
question consider forming a random rectangle in two ways let u1 u2 and u3 be independent random variables uniform on 0
question a point is generated on a unit disk in the following way the radius r is uniform on 0 1 and the angle is
question suppose that conditional on n x has a binomial distribution with n trials and probability p of success and
question spherical particles whose radii have the density function frr are dropped on a mesh as in problem find an
question let fx 6x21 - x2 for -1 le x le 1a describe an algorithm to generate random variables from this density using
question show that the number of iterations necessary to generate a random variable using the rejection method is a
question one of the most commonly used but not one of the best methods of generating pseudorandom numbers is the linear
question an urn contains p black balls q white balls and r red balls and n balls are chosen without replacementa find
question three players play 10 independent rounds of a game and each player has probability 12 of winning each round
question a sieve is made of a square mesh of wires each wire has diameter d and the holes in the mesh are squares whose
question buffons needle problem a needle of length l is dropped randomly on a plane ruled with parallel lines that are
question suppose that x y is uniformly distributed over the region defined by 0 le y le 1 - x2 and -1 le x le 1a find
question a point is uniformly distributed in a unit sphere in three dimensionsa find the marginal densities of the x y
question let x y be a random point chosen uniformly on the region r x y xy le 1a sketch rb find the marginal
question suppose that in a certain population individuals heights are approximately normally distributed with
question a system has independent units each of which fails with probability p the system fails only if k or more of
question this problem deals with an elementary aspect of a simple branching process a population starts with one member
question here is a simple model of a queue the queue runs in discrete time t 0 1 2 and at each unit of time the
question a player throws darts at a target on each trial independently of the other trials he hits the bulls-eye with
question this problem introduces some aspects of a simple genetic model assume that genes in an organism occur in pairs
question many human diseases are genetically transmitted for example hemophilia or tay-sachs disease here is a simple
question if a parent has genotype aa he transmits either a or a to an offspring each with a 12 chance the gene he
question an experiment consists of throwing a fair coin four times find the frequency function and the cumulative