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For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

P(L > 10000) Following above procedure In T –u Z = In 10000-9.3790 = -1.0187 0.1655 P(Z) = 0.1538 P(L>10000) = 1 – P(L<10000) = 1 –- 0.1538 = 0.846 P(L=12000 | L>10000) = 0.468 * 1/ 0.846 = 0.55324
Transcribed Image Text:P(L > 10000) Following above procedure In T –u Z = In 10000-9.3790 = -1.0187 0.1655 P(Z) = 0.1538 P(L>10000) = 1 – P(L<10000) = 1 –- 0.1538 = 0.846 P(L=12000 | L>10000) = 0.468 * 1/ 0.846 = 0.55324
Prob 2.37 - The life of a light bulb is lognormally distributed with mean of 12,000 h and standard deviation of 2000 h. Compute the probability that a) A light bulb will last 12,000h b) A light that has already worked for 10,000 h will last 12,000 h ANS: Given Hy = 12000, oy = 2000 He= In = 9.379 1+0*o O *0 Of = In | =0.1655 Р(В> 12000) First we have find Z values for which from the tables we get P(B<12000). In T-H Z = In 12000-9.3790 = 0.0827 0.1655 P(Z=0.0827) = 0.532 P(B>12000) = 1 - P(B<12000) = 1 - 0.532 = 0.468 P(L=12000 | L>10000) P(L=12,000)× P (L>10,000V L=12,000) P(L>10000)
Transcribed Image Text:Prob 2.37 - The life of a light bulb is lognormally distributed with mean of 12,000 h and standard deviation of 2000 h. Compute the probability that a) A light bulb will last 12,000h b) A light that has already worked for 10,000 h will last 12,000 h ANS: Given Hy = 12000, oy = 2000 He= In = 9.379 1+0*o O *0 Of = In | =0.1655 Р(В> 12000) First we have find Z values for which from the tables we get P(B<12000). In T-H Z = In 12000-9.3790 = 0.0827 0.1655 P(Z=0.0827) = 0.532 P(B>12000) = 1 - P(B<12000) = 1 - 0.532 = 0.468 P(L=12000 | L>10000) P(L=12,000)× P (L>10,000V L=12,000) P(L>10000)
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