rec15 - Massachusetts Institute of Technology Department of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 15 October 28, 2010 1. Problem 6.14 (a)-(c),(h)-(j), page 330 in text. Beginning at time t = 0, we begin using bulbs, one at a time, to illuminate a room. Bulbs are replaced immediately upon failure. Each new bulb is selected independently by an equally likely choice between a type-A bulb and a type-B bulb. The lifetime, X , of any particular bulb of a particular type is a random variable, independent of everything else, with the following PDF: for type-A Bulbs: f X ( x ) = braceleftbigg e- x , x ≥ , , otherwise; for type-B Bulbs: f X ( x ) = braceleftbigg 3 e- 3 x , x ≥ , , otherwise. (a) Find the expected time until the first failure. (b) Find the probability that there are no bulb failures before time t . (c) Given that there are no failures until time t , determine the conditional probability that the first bulb used is a type-A bulb.first bulb used is a type-A bulb....
View Full Document

This note was uploaded on 12/02/2011 for the course ENGINEERIN EE302 taught by Professor Proasin during the Spring '11 term at South Carolina.

Ask a homework question - tutors are online