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a fair coin is tossed n times let tnnbspbe the number of times in the n tosses that a tail is followed by a head show
an ordered sample of size 5 is drawn without replacement from an urn containing 8 white balls and 4 black balls for j
an urn contains 12 balls of which 8 are white and 4 are black a ball is drawn and its color noted the ball drawn is
let x1nbspand x2nbspbe the coordinates of 2 points randomly chosen on the unit interval let y x1nbsp- x2 be the
let x1nbspand x2nbspbe independent normally identically distributed random variables with mean m and variance sigma2
let x1nbspand x2nbspbe jointly normally distributed with mean 0 variance i and covariance p find emax x1
prove that if x1nbspand x2nbspare jointly normally distributed random variables whose correlation coefficient vanishes
let x1nbspand x2nbspbe jointly distributed random variables possessing finite second moments state conditions under
suppose that n tickets bear arbitrary numbers x1 x2xnnbsp which are not all the same suppose further that 2 of the
suppose that customers enter a certain shop at the rate of 30 persons an hour i what is the probability that during a
suppose that the telephone calls coming into a certain switchboard obey a poisson probability law at a rate of 16 calls
in a large fleet of delivery trucks the average number inoperative on any day because of repairs is 2 two standby
major motor failures occur among the buses of a large bus company at the rate of2 a day assuming that each motor
consider a restaurant located in the business section of a city how many seats should it have available if it wishes to
for each of the following numerical valued random phenomena state conditions under which it may be expected to obey
consider a radar set of a type whose failure law is exponential if radar sets of this type have a failure rate lambda
the lifetime in hours of a radio tube of a certain type obeys an exponential law with parameter i lambda 1000 ii
the customers of a certain newsboy arrive in accordance with a poisson probability law at a rate of 1 customer per
suppose that a certain digital computer which operates 24 hours a day suffers breakdowns at the rate of 025 per hour we
assume that the probability of failure of a ball bearing at any revolution is constant and equal to p what is the
a lepidopterist wishes to estimate the frequency with which an unusual form of a certain species of butterfly occurs in
consider a shop at which customers arrive at random at a rate of 30 per hour what fraction of the time intervals
in 10000 independent tosses of a coin 5075 heads were observed find approximately the probability of observing i
consider a room in which 730 persons are assembled for i 12 730 let ainbspbe the event that the ith person was born
plot the probability mass function of the binomial probability law with parameters n 10 and p frac12 against its