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for a given n ge 2 consider the family of binomial distributions for the number k of successes in n independent trials
suppose that y has a poisson distribution py k e-lambdalambdak k k 0 1 suppose y can be observed only when y ge 1
1 the tax rate of 0984 in decimal can be expressed as how many millsa 9840b 9084c 984d 9842 commissions charged on the
the usual sample variance s2 is a u -statistic of order 2 for n 4 x1 x2 - x3 - x424 is another possible estimator of
1 if a car is depreciated in four years what is the rate of depreciation using twice the straight-line ratea 25b 100c
1nbsp let p be a law on a separable normed vector space s middot x isin s and px the translate of p by x so that
1 a 40000 loan at 4 dated june 10 is due to be paid on october 11 calculate the amount of interest assume ordinary
show that there exist three laws alpha beta and gamma on r2 such that there is no law p on r6 with coordinates x y and
1 show that if s is the real line r with usual metric then theorem 1172 holds for the probability space 0 1 with
given a product x iti isini xi of topological spaces xi t with product topology and a directed set j a net in x
4 if x t and y u are topological spaces a is a base for t and b is a base for u show that the collection of all
1 ifnbspsinbspare sets with discrete topologies show that the product topology for finitely many such spaces is also
for any two real numbers u and v maxu v u iff u ge v otherwise maxu v v a metric space s d is called an ultrametric
1 a let q be the set of rational numbers show that the riemann integral of 1q from 0 to 1 is undefined the net in its
1 let x d and y e be pseudometric spaces with topologies td and te metrized by d and e respectively let f be a function
1 on r2 let dx y u v x - u2 y - v212 usual metric ex y x - u y - v show that e is a metric and metrizes the same
let a and b be two sets such that there exists a function f from a onto b and a function g from b onto a show assuming
1 show assuming ac that any cartesian product of finite sets is either finite or uncountable cant be countably
1 in the partially ordered set n times n with the ordering j k le m n iff j le m and k le n consider the sequence n
1 prove without applying theorem 151 that the well-ordering principle implies ac caution is it clear that the
if x is uncountable and y is a countable subset of x show that x y has the same cardinality as x assuming that n has
1 prove that for any countably infinite set s there is a 1-1 function from n onto s hint let h be a function from n
1 to define the factorial function f n n by simple recursion how can c and h in corollary 133 be chosen for h to
1 for any two relations e and f on the same set x define a relation g e f by xgz iff for some y xey and
1 an amount of r25 000 is invested at an interest rate of 11 per annum compounded half-yearly fornnbspyears find the