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numerical integration suppose that g is a non-negative continuous function on the unit interval and that supxnbspgx le
a stick of length 1 is randomly broken which means that the remaining piece is u0 1-distributed the remaining piece is
these proofs lean on the central limit theorem and cramrs theorem an alternative would be to exploit the deeper
suppose that xnnbspisin gepn n ge 1 and that x1 x2 are independent state and prove the analog of the previous
check the last claim that is prove that if x1 x2 are symmetric random variables such that xnnbsprarr a for some
can you find a sequence of absolutely continuous random variables that converges distribution to a discrete random
prove the lemmalet cn n ge 1 be a sequence of real numbers if for every subsequence there exists a further subsequence
suppose that the moments of the random variable x are constant that is suppose that e xn c for all n ge 1 for some
suppose that the mean vector and the covariance matrix of the three dimensional normal random vector x arerespectively
find the mean and variance of the binomial poisson uniform exponential gamma and standard normal
let x isin n0 1 let z be a coin-tossing random variable independent of x pz 1 pz -1 frac12 set y z middot x prove
compute the generating function of some standard distributions such as the binomial geometric and poisson
compute the moment generating function of some standard distributions such as the binomial geometric poisson
find the mean and variance of the binomial poisson uniform exponential and standard normal
check that these distributions have the desired property that is of lacking a moment generating
suppose that px 1 px -1 12 that y isin u-1 1 and that x and y are independenta show by direct computation that x y
let x x1 x2 be independent identically distributed random variables such that px 0 px 1 12a let n1nbspbe the
recall from subsection 2164 the likelihood ratio statistic ln which was defined as a product of independent identically
show that if x and y are independent identically distributed random variables then x - y has a symmetric
compute the expected number of trials needed in order for all faces of a symmetric die to have appeared at least
the coupon collectors problem each time one buys a bag of cheese doodles one obtains as a bonus a picture hidden inside
we have not explicitly proved that the base 4 example produces a continuous singular distribution please check that
prove that if x and y are independent then the conditional distributions and the unconditional distributions are the
susan has a coin with phead p1nbspand john has a coin with phead p2 susan tosses her coin m times each time she