HW 7 Solutions

# HW 7 Solutions - Steven Weber Dept of ECE Drexel University...

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Unformatted text preview: Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Homework 7 Solutions Question 1: Exercise 5, § 4.1, p.135 A college professor never finishes his lecture before the end of the hour and always finishes his lecture within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is f ( x ) = kx 2 , ≤ x ≤ 2 , otherwise (1) a. Find the value of k and draw the corresponding density curve. [Hint: Total area under the graph of f ( x ) is 1 .] Z 2 kx 2 d x = k 3 x 3 2 = k · 8 3 = 1 ⇔ k = 3 8 . (2) b. What is the probability that the lecture ends within 1 minute of the end of the hour? P ( X ≤ 1) = Z 1 3 8 x 2 d x = 1 8 x 3 1 = 1 8 . (3) c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? P (1 ≤ X ≤ 3 / 2) = Z 3 / 2 1 3 8 x 2 d x = 1 8 x 3 3 / 2 1 = 1 8 3 2 3- 1 3 ! = 19 64 (4) d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? P (3 / 2 ≤ X ≤ 2) = Z 2 3 / 2 3 8 x 2 d x = 1 8 x 3 2 3 / 2 = 1 8 2 3- 3 2 3 ! = 37 64 (5) Question 2: Exercise 22, § 4.2, p.144 The weekly demand for propane gas (in 1000 s of gallons) from a particular facility is an rv X with pdf f ( x ) = 2 ( 1- 1 x 2 ) , 1 ≤ x ≤ 2 , otherwise (6) a. Compute the cdf of X ....
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HW 7 Solutions - Steven Weber Dept of ECE Drexel University...

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