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HW7-2

HW7-2 - the lifetime of chip 2 The question is asking you...

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ECE 302, Homework #7. Due date: 3/2 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 The chain rule: Question 1: Consider the following functions. F ( x ) = Z x 0 f ( s ) ds g ( x ) = F ( h ( x )) = Z h ( x ) 0 f ( s ) ds Express d dx F ( x ) and d dx g ( x ) using f ( x ) and h ( x ). (Hint: You should use the chain rule that d dx g ( x ) = d ds F ( s ) s = h ( x ) × d dx h ( x ).) Question 2: Problem 3.45. Question 3: Problem 3.46, for which we use X to denote the lifetime of chip 1 and Y for
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Unformatted text preview: the lifetime of chip 2. The question is asking you which probability P ( X > 20000) and P ( Y > 20000) is larger? Repeat the same question for “24000 hours.” You may have to use the Q ( x ) = 1-Φ( x ) function listed in Table 3.4.s Question 4: Consider a random variable X with the corresponding pdf being f X ( x ) = . 5 e-| x | . Y = min( X, 0). Find out the cdf and pdf of Y . Question 5: Suppose X is uniformly randomly distributed between (0 , 1). Y = √ x . Find out the cdf and pdf of Y ....
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