19. The time (in hours) of electric lamps produced by a certain firm is a random variable with p.d.f f(x) : = ae-a(x-8) x > B, a, B > 0 where B is known and a is the reciprocal of the mean life time. (a) Show that the probability, g(T) that a lamp selected at random has a life time exceeding T hours, is g(T) = e¯a(T-8). (b) To estimate the value of a, a sample ofN lamp are tested but, to save sampling cost, the failure times of individual lamps are not recorded. Instead, the testing is stopped after T hours and the number of lamps which have failed within this period recorded. Denote this number by X. Use the frequency substitution principle to obtain an estimator of g(T) and hence of a. (c) Suppose 1500 lamps were tested and 108 failed when the testing is stopped, find an estimate for g(T) and hence of a given that B = 30

19. The time (in hours) of electric lamps produced by a certain firm is a random variable with p.d.f f(x) : = ae-a(x-8) x > B, a, B > 0 where B is known and a is the reciprocal of the mean life time. (a) Show that the probability, g(T) that a lamp selected at random has a life time exceeding T hours, is g(T) = e¯a(T-8). (b) To estimate the value of a, a sample ofN lamp are tested but, to save sampling cost, the failure times of individual lamps are not recorded. Instead, the testing is stopped after T hours and the number of lamps which have failed within this period recorded. Denote this number by X. Use the frequency substitution principle to obtain an estimator of g(T) and hence of a. (c) Suppose 1500 lamps were tested and 108 failed when the testing is stopped, find an estimate for g(T) and hence of a given that B = 30

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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