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consider binary splitting that is the branching process where the distri- bution of y the number of children is given
the growth dynamics of pollen cells can be modeled by binary splitting as follows after one unit of time a cell either
1 suppose that x is a nonnegative integer-valued random variable and let n and m be nonnegative integers show that
at a certain black spot the number of traffic accidents per year follows a po10 000-distribution the number of deaths
1 philip throws a fair die until he obtains a four diane then tosses a coin as many times as philip threw his die
1 lisa shoots at a target the probability of a hit in each shot is 12 given a hit the probability of a bulls-eye is p
a miner has been trapped in a mine with three doors one takes him to freedom after one hour one brings him back to the
suppose that x1 x2 are independent identically linnikalpha-distributed random variables that n isin fsp and that n
a point p is chosen uniformly in an n-dimensional sphere of radius 1 next a point q is chosen uniformly within the
let p be the probability that the tip points downward after a person throws a drawing pin once annika throws a drawing
letnbspxnbspbe the number of coin tosses until heads is obtained suppose that the probability of heads is unknown in
1 let x and y be jointly distributed random variables such that y x x isin binn x with x isin u 0 1compute e y
1 show that an exponential random variable such that the inverse of the parameter is gamma-distributed is
show that a suitable power of a weibull-distributed random variable whose parameter is gamma-distributed is
100 people are given a standard antibiotic to treat an infection and another 100 are given a new antibiotic in the rst
get the data on eruption times and waiting times between eruptions of the old faithful geyser from the website estimate
data on the magnitudes of earthquakes near fiji are available on the website for this book estimate the cdf f x compute
suppose we generate a random variable x in the following way first we ip a fair coin if the coin is heads take x to
1 suppose we play a game where we start with c dollars on each play of the game you either double or halve your
1 let x and y be independent and suppose that each has a uniform0 1 distribution let z minx y find the density fz
1 suppose a coin has probability p of falling heads up if we ip the coin many times we would expect the proportion of
1 for xednbspbnbspsuch that pbnbspgtnbsp0 show that pmiddotb satises the axioms of probability2 younbsp havenbsp
here is a method callednbspaccept-reject samplingnbspfor drawing observa- tions from a distributiona suppose
get the data on fragments of glass collected in forensic work from the book website estimate the density of the rst
letnbspx1nbspx4 be binary draw the independence graphs corresponding to the following log-linear models also identify