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a node in a communication network receives data packets of variable length each packet has a random number of bits that
the number of cars approaching a toll booth in a minute follows a geometric random variable with a mean of 2 carsminute
letnbspnbspbe a random sum of discrete iid random variablesfurther letnbspnbspbe the probability-generating functions
a gambler plays a game of chance where he wins 1 with probability and loses 1 with probability 1-p each time he plays
suppose we form a sample variancenbspfrom a sequence of iid gaussian random variables and then form another sample
letnbsp x ynbsp z and be independent gaussian random variables with equal means of micro 3 and
a player engages in the following dice tossing game craps two dice are rolled if the player rolls the dice such that
letnbspnbsp be a sequence of iid random variables uniformly distributed over suppose we form the sumnbspfirst find the
a discrete random process x n is generated by repeated tosses of a coin let the occurrence of a head be denoted by 1
let wnnbspbe an iid sequence of zero-mean gaussian random variables with variancenbspnbspdefine a discrete-time random
question 1 if a study has 3 groups of 25 subjects each the degrees of freedom are 2 and 24a trueb falsequestion 2 it is
a prove that any sequence that converges in the mean square sense must also converge in probability hint use markovs
consider a sequence of iid random variablesnbspnbspeach with cdfnbspthis sequence clearly converges in distribution
a show by counterexample that convergence almost everywhere does not imply convergence in the ms senseb show by
consider the random sequencenbspnbspwhere is a cauchy random variable with pdfnbspdetermine which forms of convergence
let xnnbspbe a sequence of iid gaussian random variables form a new sequence according todetermine which forms of
letnbspnbspbe a sequence of iid random variables with finite mean and variance show that the sequence of sample
supposenbsp xknbspis a sequence of zero-mean gaussian random variables with covariances described bynbspnbspform the
supposenbspnbspis a sequence of iid positive random variables definenbspnbspnbspnbspnbspnbspshow that
letnbspnbspbe a sequence of iid random variables with finite mean micro and let snnbspbe the sequence of sample meansa
prove that the sequence of sample means of iid random variables converges in the ms sensewhat conditions are required
letnbspnbspnbspbe a sequence of iid cauchy random variables witha show that snnbspalso follows a cauchy distributionb
independent samples are taken of a random variable x if the pdf of is uniform over the intervalnbspnbspand zero
consider the lottery described in given exercisea assuming six million tickets are sold and that each player selects
a communication system transmits bits over a channel such that the probability of being received in error is p002 bits