QUESTION 12 The lifetime X of an item is normally distribute with mean = 7 years

Question

QUESTION 12 The lifetime X of an item is normally distribute with mean = 7 years and standard deviation 2 years. Consider an insurance policy that insures the item against early failure. In particular, the insurance will pay C dollars if the item fails within the first two years and nothing if the item fails after second year. Find the value of C such that the expected insurance payment is $50. 50 e 51 o 8063 e 8065 QUESTION 13 The random variables Ni, X2, and Xs are Stochastic Independent with respective means 9. 1, and 16 and respective variances 64. 49, and 25. If -11, 40 -11, 138 21. 40 21. 138

Explanation / Answer

The value of C is evaluated as 50=C*P(x<=2) the z value is (2-7)/2=-2.5, thus C=50/P(z<=-2.5)=50/0.0062=8064.51, thus 8065 is the answer.

The mean is simply 9-4+16=21 and the variance=(64+49+25)=138. Thus answer is 21,138

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