hw5 - AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY...

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Unformatted text preview: AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 5 Due at the beginning of class on Thursday, October 29, 2009. Reminder: Show your reasoning! Read: Ross, Chapter 5, Sections 5.1–5.5, 5.7. (You may skip section 5.5.1 on hazard rate functions.) (1). [Related to Example 5b (Ross, Chap 5), and exercises 32, 33 (Ross, Chap 5).] (15 points) The lifetime (in hours) of a lightbulb is an exponentially distributed random variable with parameter λ = 0 . 10 (units of hours- 1 ). (a). What is the probability that the light bulb is still burning one day after it is installed? (b). Assume that the bulb was installed at noon today and assume that at 3:00pm today you notice that the bulb is still working. (i). What is the chance that the bulb will burn out at some time between 4:30pm and 6:00pm today? (ii). What is the expected time when the bulb burns out? (again, given that it was still working at 3:00pm today) (2). (20 points) [Related to Example 1d and Examples 7a, 7b, 7c, 7d (Ross), and exercises 37, 39–41, and theoretical...
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This note was uploaded on 02/07/2010 for the course AMS 311 taught by Professor Tucker,a during the Fall '08 term at SUNY Stony Brook.

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