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we stressed the importance of the mean of a rv x in terms of its associ- ation with the sample average via the wlln
represent the mgf of a rvnbspxnbspby gxnbspr r 0 erxdfx -infin r infinnbsperxdfxin each of the following parts you
consider a discrete rv x with the pmfpx -1 1 - 10-102px 1 1 - 10-102px 1012 10-10a find the mean and variance of x
exercise 21a find the erlang density f sn t by convolving fx x lambda exp-lambdax with itself n timesb find the
the point of this exercise is to show that the sequence of pmfs for a bernoulli counting process does not specify the
an elementary experiment is independently performed n times where n is a poisson rv of mean lambda let a1 a2 ak be
starting from time 0 northbound buses arrive at 77 mass avenue according to a poisson process of ratenbsplambda
consider generalizing the bulk arrival process in figure 25 assume that the epochs at which arrivals occur form a
consider a counting process in which the rate is a rvnbspetanbspwith probability density fetalambda
a use 242 to find e si ntn hint when you integrate sifsi si ntn compare this integral with fsi1 si ntn 1 and use
suppose cars enter a one-way infinite length infinite lane highway at a poisson rate lambda the ith car to enter
consider an mginfin queue ie a queue with poisson arrivals of rate lambda in which each arrival i independent of other
the voters in a given town arrive at the place of voting according to a poisson process of rate lambda 100 voters per
let n1tnbspt gtnbsp0 be a poisson counting process of ratenbsplambda assume that the arrivals from this process are
let us model the chess tournament between fisher and spassky as a stochastic process let xi for i ge 1 be the duration
this problem is intended to show that one can analyze the long-term behavior of queueing problems by using just notions
the purpose of this problem is to illustrate that for an arrival process with independent but not identically
let q be an orthonormal matrix show that the squared distance between any two vectors z and y is equal to the squared
a let w be a normalized iid gaussian n-rv and let y be a gaussian m-rv suppose we would like the joint covariance e
let x and z be statistically independent gaussian rv s of arbitrary dimension n and m respectively let y hx z where h
show that every markov chain with m ltgtinfin states contains at least one recurrent set of states explaining each of
proof of theorem 4211 anbspshow that an ergodic markov chain with m states must contain a cycle withnbsptau ltgtm
a find the steady-state probabilities for each of the markov chains in figure 42 assume that all clockwise
consider a finite-state markov chain with matrix p which has kappa aperiodic recurrent classes r 1 r kappa and a set
answer the following questions for the following stochastic matrix pp 1212001212001a find pn in closed form for