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consider a utility function u for which uo 0 and uioo - i suppose that a person who has this utility function is
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