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sFinal_06S - ECE 302 Final 3:20-5:20pm Mon May 1 WTHR 160...

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Unformatted text preview: ECE 302, Final 3:20-5:20pm Mon. May 1, WTHR 160 or WTHR 172. 1. Enter your name, student ID number, e-mail address, and signature in the space provided on this page, NOW! 2. This is a closed book exam. 3. This exam contains 7 questions and is worth 100 points + 18 bonus points. You have two hours to complete it. So basically, you only need to answer ≈ 5–6 questions correctly to get full grade. I will suggest not spending too much time on a single question, and work on those you know how to solve. 4. The sub-questions of a given question are listed from the easiest to the hardest. The best strategy may be to finish only the sub-questions you know exactly how to solve. 5. Write down as much your knowledge about how to solve the problem. You might get some partial credit. 6. There are a total of 14 pages in the exam booklet. Use the back of each page for rough work. 7. Neither calculators nor help sheets are allowed. 8. Read through all of the problems first, and consult with the TA during the first 20 minutes. After that, no questions should be asked unless under special circum- stances, which is at TA’s discretion. You can also get a feel for how long each question might take after browsing through the entire question set. Good luck! Name: Student ID: E-mail: Signature: Bernoulli distribution with parameter p : P ( X = 0) = 1- p, P ( X = 1) = p E ( X ) = p Var ( X ) = p (1- p ) . Poisson random variable (Poisson distribution) with parameter λ : P ( X = k ) = λ k k ! e- λ , ∀ k ∈ { , 1 , ··· ,n, ···} E ( X ) = λ Var ( X ) = λ. Geometric random variable (geometric distribution) with parameter p : P ( X = k ) = p (1- p ) k , ∀ k ∈ { , 1 , ··· ,n, ···} E ( X ) = 1- p p Var ( X ) = 1- p p 2 . Gaussian random variable (Gaussian distribution) with parameters ( m,σ 2 ): f ( x ) = 1 √ 2 πσ 2 e- ( x- m ) 2 2 σ 2 E ( X ) = m Var ( X ) = σ 2 . Discrete Fourier transform: S ( f ) = F ( R ( n )) = ∞ summationdisplay n =-∞ R ( n ) e- 2 πfn . Continuous Fourier transform: S ( f ) = F ( R ( t )) = integraldisplay ∞ t =-∞ R ( t ) e- 2 πft . Question 1: (20%) Suppose X is the result of tossing a fair die with 6 faces, namely, P ( X = i ) = 1 / 6 for i = 1 , ··· , 6. Another computer program independently generates a6....
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sFinal_06S - ECE 302 Final 3:20-5:20pm Mon May 1 WTHR 160...

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