A flood-control system is designed such that the probability of the system capacity being exceeded X times in 30 years is given in the following table. What is the mean number of system failures expected in 30 years? What are the variance and skewness of the number of failures? X₁ f(x₁) 0.04 0.14 0.23 0 1 2 3 4 5 6 7 8 9+ 0.24 0.18 0.1 0.05 0.02 0.01 0.00

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A flood-control system is designed such that the probability of the system capacity being
exceeded X times in 30 years is given in the following table. What is the mean number of system
failures expected in 30 years? What are the variance and skewness of the number of failures?
X₁
f(x₁)
0.04
0.14
0.23
0.24
0.18
0.1
0.05
0.02
0.01
0.00
0
1
2
3
4
5
6
7
8
9+
00
Transcribed Image Text:A flood-control system is designed such that the probability of the system capacity being exceeded X times in 30 years is given in the following table. What is the mean number of system failures expected in 30 years? What are the variance and skewness of the number of failures? X₁ f(x₁) 0.04 0.14 0.23 0.24 0.18 0.1 0.05 0.02 0.01 0.00 0 1 2 3 4 5 6 7 8 9+ 00
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