HW5-2

# HW5-2 - Problems 3.2 and 3.7 Question 4 Problem 3.15a After...

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ECE 302, Homework #5. Due date: 2/16 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: [email protected] Oﬃce: MSEE354 Oﬃce Hours: MWF: 12pm–1pm TA: Kamesh Krishnamurthy, Email: [email protected] Oﬃce: POTR 370 Oﬃce Hours: M: 10–11am TTh: 10:30am–12:30pm Review of Calculus: Question 1: Deﬁne a 1-D function f ( x ) as follows. f ( x ) = ( 3 e - 3 x if x [0 , ) 0 otherwise Let F ( x ) = R x -∞ f ( s ) ds . Compute the following values in terms of x or k . 1. F ( x ) if x < 0. 2. F ( x ) if x [0 , ). 3. lim x →∞ F ( x ). 4. For any integer value k , let p k = R 1 . 5( k +1) 1 . 5 k f ( s ) ds . Find the value of p k . Question 2: Plug in the values that p 1 = 2 / 3 and p 2 = 1 / 3, and solve Problem 2.94a and 2.94b. (You are welcome to try 2.94c for your own interest, but there is no need to turn in the solutions of 2.94c.) Question 3:

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Unformatted text preview: Problems 3.2 and 3.7. Question 4: Problem 3.15a. After ﬁnishing 3.15a, ﬁnd the pdf f Y ( y ) of the random variable Y . Then complete 3.15b by using f Y ( y ). Question 5: (Very similar to Problem 3.16) Suppose the cdf F X ( x ) of a random variable X is as follows. F X ( x ) = if x <-π/ 2 c (1 + sin( x )) if-π/ 2 ≤ x < π/ 2 1 if π/ 2 ≤ x 1. Explain why c cannot be 1? 2. Explain why when c = 1 / 2, X is a continuous random variable. (Hint: you should check whether there is any jump or not.) 3. Let c = 1 / 4. Find the generalized pdf of X using the δ function. Question 6: Problem 3.20. Question 7: Problem 3.22....
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• Spring '08
• GELFAND
• Probability distribution, Probability theory, probability density function, Cumulative distribution function, Continuous probability distribution

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HW5-2 - Problems 3.2 and 3.7 Question 4 Problem 3.15a After...

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