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1 we have seen that a thinned poisson process is again a poisson-process prove the following analog for a geometric
1 consider a sender that transmits signals according to a poisson process with intensitynbsplambda the signals are
mans waits for the bus the waiting time t until a bus comes is u 0 a- distributed while he waits he tries to
karin arrives at the post office which opens at 900 am at 905 am she finds two cashiers at work both serving one
a specific component in a cryptometer has an expmicro-distributed life- time micro gt 0 if replacement is made as soon
1 consider a poisson process with intensity lambda we start observing at time t 0 let t be the time that has
at the center of espionage in kznatropsk one is thinking of a new method for sending morse telegrams instead of using
fredrik and ulrich both received soap bubble machines for christmas the machines emit bubbles according to independent
suppose that x1 x2 are independent identically linnikalpha-distributed random variables that n isin fsp and that n
let x1 x2 be independent u 0 1-distributed random variables and let nm isin pom be independent of x1 x2 set vm
1 let x1 x2 be independent la-distributed random variables and let n isin pom be independent of x1 x2 determine
1 let x and y be jointly normal with means 0 variances 1 and correlation coefficient rho compute the moment generating
1 suppose that the random variables x and y are independent and n 0 sigma2- distributeda show that xy isin c0 1b
1 the random vector x y t has a two-dimensional normal distribution with var x var y show that x y and x - y are
1 letnbspx1nbspx2nbsp x8 be independent exp1-distributed random variables with order statistic x1 x2 x8 find
suppose that x1 x2 x3 are independent u 0 1-distributed random variables and let x1 x2 x3 be the corresponding order
suppose that x1 x2 x3 x4 are independent u 0 1-distributed random variables and let x1 x2 x3 x4 be the corresponding
1 let x1 x2 x3 and x4 be independent u 0 1-distributed random variables computea p x3 x4 le 1b p x3 x4 le 12 let x1
1 the statistician piggy has to wait an amount of timenbspt0 at the post office on an occasion when she is in a great
1 suppose that x y and z have a joint density function given by e-xyz for x y z gt 0 f x y z 0
consider a branching process with a pom-distributed offspring let x1 and x2 be the number of individuals in generations
let xn be the number of individuals in the nth generation of a branching process x0 1 and set tn 1 x1 middot middot
1 consider a branching process with reproduction meannbspmnbsp1 suppose also as before thatnbspx0 1a what is the
letnbspxn nnbspgenbsp0nbspbe the usual galton-watson process starting with x0 1 suppose in addition that immigration
consider the following modification of a branching process a mature individual produces children according to the