Q3 Let N(t) be the number of failures of a computer system on the interval [0, t]. We suppose that {N(t),t >0} is a Poisson process with rat A =1 per week. Q3 (i.) Calculate the probability that the system functions without failure during two consecutive weeks. Q3 (ii.) Calculate the probability that the system has exactly two failures during a given week, knowing it has functioned without failure during the previous two weeks. Q3 (iii.) Calculate the probability that less than two weeks elapse before the third failure occurs. Q3 (iv.) Let Z(t) = e N€), for t>0. Show that E[Z(t]] = exp[t(e1 – 1)] using conditioning arguments.
Q3 Let N(t) be the number of failures of a computer system on the interval [0, t]. We suppose that {N(t),t >0} is a Poisson process with rat A =1 per week. Q3 (i.) Calculate the probability that the system functions without failure during two consecutive weeks. Q3 (ii.) Calculate the probability that the system has exactly two failures during a given week, knowing it has functioned without failure during the previous two weeks. Q3 (iii.) Calculate the probability that less than two weeks elapse before the third failure occurs. Q3 (iv.) Let Z(t) = e N€), for t>0. Show that E[Z(t]] = exp[t(e1 – 1)] using conditioning arguments.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 27E
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![Q3 Let N(t) be the number of failures of a computer system on the interval [0, t]. We suppose that {N(t),t > 0}
is a Poisson process with rat A=1 per week.
Q3 (i.) Calculate the probability that the system functions without failure during two consecutive weeks.
Q3 (ii.) Calculate the probability that the system has exactly two failures during a given week, knowing it has
functioned without failure during the previous two weeks.
Q3 (iii.) Calculate the probability that less than two weeks elapse before the third failure occurs.
Q3(iv.) Let
Z(t) = eN(t),
t> 0.
for
Show that
E[Z(t]] = exp{t(e – 1)]
using conditioning arguments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Fcf1f2eea-0a12-4e4e-b3e3-97c8d194fe2d%2Frb66utp_processed.png&w=3840&q=75)
Transcribed Image Text:Q3 Let N(t) be the number of failures of a computer system on the interval [0, t]. We suppose that {N(t),t > 0}
is a Poisson process with rat A=1 per week.
Q3 (i.) Calculate the probability that the system functions without failure during two consecutive weeks.
Q3 (ii.) Calculate the probability that the system has exactly two failures during a given week, knowing it has
functioned without failure during the previous two weeks.
Q3 (iii.) Calculate the probability that less than two weeks elapse before the third failure occurs.
Q3(iv.) Let
Z(t) = eN(t),
t> 0.
for
Show that
E[Z(t]] = exp{t(e – 1)]
using conditioning arguments.
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