2011_175HWSet3 - THE UNIVERSITY OF IOWA 22S:175 Write...

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THE UNIVERSITY OF IOWA 22S:175 H.W. Set #3 Due at the beginning of class on Monday, February 7, 2011 Write legibly. Show your steps. Explain your reasoning. Simplify your answers. Each question is worth 10 points 1. Hogg, McKean & Craig (2005) Intro to Math Stat , 6 th edition, page 157 #3.3.5. Remarks : (i) This result can also be found in Actuarial Mathematics and in Introduction to Probability Models . (ii) If you use the anti-derivative in the Hint, you should first show that it is indeed an anti-derivative; otherwise, points will be deducted. 2. (An old SOA exam question) A Mars probe has n batteries. Once a battery is activated, its future lifetime is exponential with mean years. The first battery is activated when the probe lands on Mars. The second battery is activated when the first fails. The third battery is activated when the second fails, and so on. Battery lifetimes after activation are independent. The probe transmits data until all n batteries have failed.
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2011_175HWSet3 - THE UNIVERSITY OF IOWA 22S:175 Write...

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