The earthwork for a construction project could take 2 or 3 months with probabili

Question

The earthwork for a construction project could take 2 or 3 months with probabilities of 0.4 and 0.6, respectively. Foundation work could take 3 or 4 months with probabilities of 0.7 and 0.3, respectively. Building the superstructure could take 5 or 7 months, with equal probabilities. Assume that the construction stages are statistically independent and must be completed in order (they can’t be done simultaneously). Determine and plot the probability mass function (PMF) for the total construction time of the project

Explanation / Answer

Let X be the total construction time of the project.

X can take the values:

2+3+5=10

2+3+7=12

2+4+5=11

2+4+7=13

3+3+5=11

3+3+7=13

3+4+5=12

3+4+7=14

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P(X=10) = (2,3,5) = 0.14

P(X=11) = (2,4,5) + (3,3,5) = 0.06 + 0.21 = 0.27

P(X=12) = (2,3,7) + (3,4,5) = 0.14 + 0.09 = 0.23

P(X=13) = (2,4,7) + (3,3,7) = 0.06 + 0.21 = 0.27

P(X=14) = (3,4,7) = 0.09

Cheers!

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