(6) The life in years of a certain type of electronic switch, X, has the following probabilitydensity function:f(x) = -=-e-2/², x > 0.(a) Find the value of the constant c. And compute the expected value of x.(b) Find the probability that a randomly selected switch will last more than 3 years. Inother words, find P(X > 3).(c) Given that a switch has been working for 1 year already, find the probability thatthe switch will last more than 3 additional years.(d) If 5 of the new switches are installed in different independent systems, what is theprobability that there will be 3 of these 5 switches fail during the first three yearsafter the installation?

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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