ECE6540Fall09Midterm1

ECE6540Fall09Midterm1 - NAME ECE 6540 MIDTERM 1 Show your...

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NAME: ECE 6540 MIDTERM 1 Show your work. Closed book, limited notes (1 page). No laptops or calculators. 1. ( 25 points ) We have N observations x [ n ] = w [ n ], n = 0 , 1 ,...N - 1 where w [ n ] is IID (independent, identically distributed) with an uniform distribution U [0 ]. (a) Show that ˆ β = 2 N N - 1 n =0 x [ n ] is an unbiased estimator for β . (b) Let σ 2 denote the unknown variance for our uniform distribution. It is known that the variance of a uniform distribution of the form U [0 ] is equal to β 2 / 12. Therefore, we could estimate σ 2 as a function of the estimator from the previous part: ˆ σ 2 = ˆ β 2 12 Is this estimator for σ 2 unbiased? What happens as N → ∞ ?
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2. ( 25 points ) A credit card company’s fraud prevention software monitors all transactions and generates an alert whenever suspicious activity is detected. Let x [ n ] denote the number of alerts generated on day number n . If we record the number of alerts for N days, x [ n ] for n
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ECE6540Fall09Midterm1 - NAME ECE 6540 MIDTERM 1 Show your...

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