CAS Exam MAS-I Fall 2018, Question 8
Study guide: Exam MAS-I
You are given the following information about a parallel system with two components:
- The first component has a lifetime that is uniform on
(0, 1) - The second component has a lifetime that is exponential with mean of 2
Determine which of the following is an expression for the expected lifetime of the system.
- A)
\int_0^1 (1-t)\, dt + \int_0^1 t\, e^{-\frac{1}{2}t}\, dt + \int_1^\infty e^{-\frac{1}{2}t}\, dt - B)
\int_0^\infty (1-t)\, e^{-\frac{1}{2}t}\, dt - C)
\int_0^1 t\, dt + \int_0^1 (1-t)(1 - e^{-\frac{1}{2}t})\, dt + \int_1^\infty (1 - e^{-\frac{1}{2}t})\, dt - D)
\int_0^\infty e^{-\frac{1}{2}t}\, dt + \int_0^1 (1-t)\, dt - \int_1^\infty (1-t)\, e^{-\frac{1}{2}t}\, dt - E)
\int_0^1 (1-t)\, dt + \int_0^\infty e^{-\frac{1}{2}t}\, dt - \int_0^\infty (1-t)\, e^{-\frac{1}{2}t}\, dt
Answer this question and see the worked solution