Quiz 1 KEY

# Quiz 1 KEY - is the relationship between P ( t ) and Q ( t...

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Name: PID: TA: Sec. No: Sec. Time: Math 10C Quiz 1 Jan 18, 2008 1. Consider a group of new lightbulbs. For a given bulb, let t be the number of months the bulb lasts before burning out. The density function for the distribution of t is given by p ( t ) = Ce - Ct for some positive constant C . a. What is the physical meaning of P ( t ) = i t 0 p ( x ) dx ? Solution: P ( t ) is the fraction of the lightbulbs which have burned out by time t . Alternatively, P ( t ) is the fraction of bulbs whose survival time lies between 0 and t months. Note that lim t →∞ P ( t ) = 1. In other words, as t increases, the fraction of the lightbulbs that have burned out approaches 1. b. Let Q ( t ) be the probability that a randomly selected bulb lasts at least t months. What
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Unformatted text preview: is the relationship between P ( t ) and Q ( t )? Find a formula for Q ( t ). Solution: Since at a given time t , every lightbulb either has burned out or still works, P ( t ) + Q ( t ) = 1. We can easily compute P ( t ) by evaluating the integral i t Ce-Ct dx . We obtain P ( t ) = 1-e-Ct . Then Q ( t ) = 1-P ( t ) = e-Ct . c. Suppose that a bulb has a 60% chance of lasting for 12 months. Find C . It is not necessarily to simplify your answer, or express it as a decimal. Solution: We need to solve Q (12) = e-12 C = 0 . 6 for the constant C . We get-12 C = ln(0 . 6) = ln(3)-ln(5). So C = ln(5)-ln(3) 12 ....
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## This test prep was uploaded on 04/11/2008 for the course MATH 10C taught by Professor Hohnhold during the Winter '07 term at UCSD.

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