For complicated projects such as construction of

Chapter , Problem 8

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For complicated projects such as construction of spacecrafts, project managers estimate two quantities, a and b, the minimum and maximum lengths of time it will take for a project to be completed, respectively. In estimating b, they consider all of the possible complications that might delay the completion date. Experience shows that the actual length of time it takes for a project to be completed is a random variable defined by Y = a + (b a)X, where X is beta with parameters and ( > 0, > 0) that can be determined for the project. (a) Find E(Y ) and Var(Y ). (b) Find the probability density function of Y . (c) Suppose that it takes Y years to complete a specific project, where Y = 2 + 4X, and X is beta with parameters = 2 and = 3. What is the probability that it takes less than 3 years to complete the project?

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