3. Let T represent the lifetime in years of a part which follows a Weibull distribution...
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3. Let T represent the lifetime in years of a part which follows a Weibull distribution with shape 2 and scale 5. For (g) through (k), additionally provide the appropriate R code. (a) What is f(t)? (b) What is F(t)? (c) What is S(t)? (d) What is h(t)? (e) What is E(T)? Make sure to simplify the gamma function in terms of pi. (f) What is V(T)? Make sure to simplify the gamma function in terms of pi. (g) What is P(T> 6)? (h) What is P(2<T<5)? (i) What is P(2 ≤ T <5)? (j) What is the 25th percentile of T? (k) What is the probability that the part is still functional at year 8, given that it was still functional at year 5? (1) For this population of parts, does it appear that the part gets weaker or stronger as time passes? You must justify your answer. 3. Let T represent the lifetime in years of a part which follows a Weibull distribution with shape 2 and scale 5. For (g) through (k), additionally provide the appropriate R code. (a) What is f(t)? (b) What is F(t)? (c) What is S(t)? (d) What is h(t)? (e) What is E(T)? Make sure to simplify the gamma function in terms of pi. (f) What is V(T)? Make sure to simplify the gamma function in terms of pi. (g) What is P(T> 6)? (h) What is P(2<T<5)? (i) What is P(2 ≤ T <5)? (j) What is the 25th percentile of T? (k) What is the probability that the part is still functional at year 8, given that it was still functional at year 5? (1) For this population of parts, does it appear that the part gets weaker or stronger as time passes? You must justify your answer.
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a The probability density function PDF of a Weibull distribution with shape parameter k and scale parameter is given by ft k t k 1 expt k In this case ... View the full answer
Related Book For
Financial Algebra advanced algebra with financial applications
ISBN: 978-0538449670
1st edition
Authors: Robert K. Gerver
Posted Date:
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