Suppose the experiment is to choose a real number at random in the interval (0, 1). For
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Suppose the experiment is to choose a real number at random in the interval (0, 1). For any subinterval (a, b) ⊂ (0, 1), it seems reasonable to assign the probability P[(a, b)] = b−a; i.e., the probability of selecting the point from a subinterval is directly proportional to the length of the subinterval. If this is the case, choose an appropriate sequence of subintervals and use expression (1.3.8) to show that P[{a}] = 0, for all a ∈ (0, 1).
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Proof To show that Pa 0 for all a 0 1 we must prove that the value of P is 0 for any subinterval of ...View the full answer
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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