19. The time (in hours) of electric lamps produced by a certain firm is a random variable with p.d.f S(z) = ae¯al=-9), 1>B, a,3 > 0 where 3 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-9). (b) To estimate the value of a , a sample of N 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 3 = 30
19. The time (in hours) of electric lamps produced by a certain firm is a random variable with p.d.f S(z) = ae¯al=-9), 1>B, a,3 > 0 where 3 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-9). (b) To estimate the value of a , a sample of N 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 3 = 30
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Transcribed Image Text:19. The time (in hours) of electric lamps produced by a certain firm is a random variable with p.d.f
f(r) = ae¯a(z-9), r> B, a,ß > 0
where 3 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-9).
(b) To estimate the value of a , a sample of N 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 3 = 30
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