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1 the probability of a royal flush in a poker hand is p 1649740 how large must n be to render the probability of
1 write a program for the user to input n p j and have the program print out the exact value of bn p k and the poisson
1 if a coin is tossed a sequence of times what is the probability that the first head will occur after the fifth toss
1 let x be a random variable which can take on countably many values show that x cannot be uniformly distributed2
let n be a positive integer let s be the set of integers between 1 and n consider the following process we remove a
suppose that we are the de- clarer in a hand of bridge and we have the king 9 8 7 and 2 of a certain suit while the
in the preceding exercise it is natural to ask how do we get the information that the given hand has an ace gridgeman
consider the two-armed bandit problem of example 424 bruce barnes pro- posed the following strategy which is a
write a program to allow you to compare the strategies play-the-winner and play-the-best-machine for the two-armed
previous experience with a drug suggests that the probability p that the drug is effective is a random quantity having
you proved the following if you take a stick of unit length and break it into three pieces choosing the breaks at
the acme super light bulb is known to have a useful life described by the density functionf t 01e-01t where time t is
here are two variations of the monty hall problem that are discussed by granberga suppose that everything is the same
physicists say that particles in a long tube are constantly moving back and forth along the tube each with a velocity
probability theory was used in a famous court casenbsppeople v collins10 in this case a purse was snatched from an
in london half of the days have some rain the weather forecaster is correct 23 of the time ie the probability that it
1 a fair coin is thrown n times show that the conditional probability of a head on any specified trial given a total of
1 one coin in a collection of 65 has two heads the rest are fair if a coin chosen at random from the lot and then
the polya urn model for contagion is as follows we start with an urn which contains one white ball and one black ball
1 prove that if a and b are independent so area a and btildeb atilde and btilde2 a doctor assumes that a patient has
1 let a b c d e f assume that ma mb 18 and mc md me mf 316 let a b and c be the events a d e a b c e a c c
1 assume that e and f are two events with positive probabilities show that if p ef p e then p f e p f 2 a coin
1 prove that the probability of exactly n heads in 2n tosses of a fair coin is given by the product of the odd numbers
let j and n be positive integers with j le n an experiment consists of choosing at random a j-tuple of positive
2n balls are chosen at random from a total of 2n red balls and 2n blue balls find a combinatorial expression for the