The article Expectation Analysis of the Probability of Failure for Water Supply Pipes (J of Pipeline Systems Engr and Practice, May 2012 36 46) proposed using the Poisson distribution to model the number of failures in pipelines of various types Suppose that for cast iron pipe of a particular lengt...

All these solutions are found using the cumulative Poi ...

The article Expectation Analysis of the Probability of Failure for Water Supply Pipes (J. of Pipeline Systems

Question:

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes" (J. of Pipeline Systems Engr. and Practice, May 2012: 36-46) proposed using the Poisson to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson with µ = 1.
a. Obtain P(X < 5) by using Appendix Table A.2.
b. Determine P(X = 2) first from the pmf formula and then from Appendix Table A.2.
c. Determine P (2 < X < 4).
d. What is the probability that X exceeds its mean value by more than one standard deviation?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...