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suppose that a person has a lottery ticket from which he will win x dollars where x has a uniform distribution on the
determine the expectation of the range of a random sample of size n from a uniform distribution on the interval 0
if m is a median of the distribution of x and if y rex is either a nondecreasing or a nonincreasing function of x show
how large a random sample must be taken from a given distribution in order for the probability to be at least 099 that
prove that if a sequence zt z2 converges to a constant b in the quadratic mean then the sequence also converges to b
suppose that 20 percent of the students who took a certain test were from school a and that the arithmetic average of
in a small community consisting of 153 families the number of families that have k children k - 0 12 is given in the
suppose that a fire can occur at any one of five points along a road these points are located at - 3 - 1 0 1 and 2 in
if n houses are located at various points along a straight road at what point along the road should a store be located
consider a coin for which the probability of obtaining a head on any given toss is 03 suppose that the coin is to be
suppose that x has a uniform distribution on the interval -2 2 and that y x show that x and y are
suppose that the random variable x has a uniform distribution on the interval 0 1 that the random variable y has a
suppose that a particle starts at the origin of the real line and moves along the line in jumps of one unit for each
suppose that on each play of a certain game a gambler is equally likely to win or to lose suppose that when he wins his
suppose that a class contains 10 boys and 15 girls and suppose that 8 students are to be selected at random from the
suppose that the proportion of defective items in a large lot is p and suppose that a random sample of ii items is
suppose that a fair coin is tossed repeatedly until a head is obtained for the first timea what is the expected number
suppose that a fair coin is tossed repeatedly until exactly k heads have been obtained determine the expected number of
suppose that one word is selected at random from the sentence the girl put on her beautiful red hat if x denotes the
for any given numbers a and b such that a lt b find the variance of the uniform distribution on the interval a
construct an example of a distribution for which the mean exists but the variance does not
suppose that x is a random variable or which pound x 1 poundx2 2 and poundx3 5 find the value o the third central
if x has a uniform distribution on the interval a b what is the value of the fifth central moment of
prove that stopping times with finite mean are regular for martingales with uniformly bounded
continuation in practice it might be of interest to determine the value of a in the previous problem in order to