The useful life, T of welding machines is assumed as a random variable having an exponential probability distribution. The pdf and CDF of T are, respectively, as follows: fr(t) eat and Fr(t) = 1-e-λt t≥0 As an illustrative example, the corresponding graphs for μT = 50 are shown, respectively, in Figs. 3.7a and 3.7b. PDF of T 0.25 0.2 0.15 Mean of T-50 0.1 0.05 CDF of T 1 0.8 0.6 Mean of T=50 0.4- 0.2 ° 0 50 100 150 Values of T 200 250 300 о (a) 50 50 100 150 Values of T (b) 200 250 300 Figure 3.7 Exponential (a) pdf and (b) CDF of useful life T of a welding machine for μT= 50 Compute mean, median, mode, variance, standard deviation and coefficient of variation of T. For the exponential distribution of the useful life of welding machines, T, of Example 3.9, the mean useful life of the machines is μT. Then, calculate the third central moment of the pdf| and the skewness
The useful life, T of welding machines is assumed as a random variable having an exponential probability distribution. The pdf and CDF of T are, respectively, as follows: fr(t) eat and Fr(t) = 1-e-λt t≥0 As an illustrative example, the corresponding graphs for μT = 50 are shown, respectively, in Figs. 3.7a and 3.7b. PDF of T 0.25 0.2 0.15 Mean of T-50 0.1 0.05 CDF of T 1 0.8 0.6 Mean of T=50 0.4- 0.2 ° 0 50 100 150 Values of T 200 250 300 о (a) 50 50 100 150 Values of T (b) 200 250 300 Figure 3.7 Exponential (a) pdf and (b) CDF of useful life T of a welding machine for μT= 50 Compute mean, median, mode, variance, standard deviation and coefficient of variation of T. For the exponential distribution of the useful life of welding machines, T, of Example 3.9, the mean useful life of the machines is μT. Then, calculate the third central moment of the pdf| and the skewness
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Transcribed Image Text:The useful life, T of welding machines is assumed as a random variable having an exponential
probability distribution. The pdf and CDF of T are, respectively, as follows:
fr(t) eat and Fr(t) = 1-e-λt
t≥0
As an illustrative example, the corresponding graphs for μT = 50 are shown, respectively, in
Figs. 3.7a and 3.7b.
PDF of T
0.25
0.2
0.15
Mean of T-50
0.1
0.05
CDF of T
1
0.8
0.6
Mean of T=50
0.4-
0.2
°
0
50
100
150
Values of T
200 250
300
о
(a)
50
50
100
150
Values of T
(b)
200
250
300
Figure 3.7 Exponential (a) pdf and (b) CDF of useful life T of a welding machine for μT= 50
Compute mean, median, mode, variance, standard deviation and coefficient of variation of T.
For the exponential distribution of the useful life of welding machines, T, of Example 3.9, the
mean useful life of the machines is μT. Then, calculate the third central moment of the pdf|
and the skewness
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