(6) The life in years of a certain type of electronic switch, X, has the following probability density function: f(x) = ²e-3/², z>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. In other words, find P(X > 3). (c) Given that a switch has been working for 1 year already, find the probability that the switch will last more than 3 additional years.
(6) The life in years of a certain type of electronic switch, X, has the following probability density function: f(x) = ²e-3/², z>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. In other words, find P(X > 3). (c) Given that a switch has been working for 1 year already, find the probability that the switch will last more than 3 additional years.
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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![The life in years of a certain type of electronic switch, \( X \), has the following probability density function:
\[
f(x) = \frac{1}{c} e^{-x/2}, \quad x > 0.
\]
(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. In other words, find \( P(X > 3) \).
(c) Given that a switch has been working for 1 year already, find the probability that the switch will last more than 3 additional years.
(d) If 5 of the new switches are installed in different independent systems, what is the probability that there will be 3 of these 5 switches fail during the first three years after the installation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1941a39f-dbc9-477a-8528-f1bffe3dd4bc%2Ffbac8a94-df7a-48bf-a03a-e5f41a587e48%2Fq6kp1n_processed.png&w=3840&q=75)
Transcribed Image Text:The life in years of a certain type of electronic switch, \( X \), has the following probability density function:
\[
f(x) = \frac{1}{c} e^{-x/2}, \quad x > 0.
\]
(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. In other words, find \( P(X > 3) \).
(c) Given that a switch has been working for 1 year already, find the probability that the switch will last more than 3 additional years.
(d) If 5 of the new switches are installed in different independent systems, what is the probability that there will be 3 of these 5 switches fail during the first three years after the installation?
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