Fall 2010 HW08

# Fall 2010 HW08 - University of Illinois Fall 2010 ECE 313:...

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University of Illinois Fall 2010 ECE 313: Problem Set 8: Solutions Linear Scaling, Gaussian Distribution, ML Parameter Estimation 1. [Gaussian Distribution] (a) As X is a continuous-type random variable, P { X = c } = 0 for any value of c including c = 0. (b) P {| X + 4 | ≥ 2 } = P { X ≤ - 6 X ≥ - 2 } = P { X ≤ - 6 } + P { X ≥ - 2 } = 2 P { X ≥ - 2 } = 2 P { X + 4 3 2 / 3 } = 2 Q (2 / 3) = 2 × 0 . 2514 = 0 . 5028 (c) P { 0 < X < 2 } = P { X > 0 } - P { X 2 } = P { X + 4 3 > 4 / 3 } - P { X + 4 3 2 } = Q (4 / 3) - Q (2) = 0 . 0 . 0918 - 0 . 0228 = 0 . 069 (d) P { X 2 < 9 } = P {- 3 < X < 3 } = P { 1 3 < X + 4 3 < 7 / 3 } = Φ(7 / 3) - Φ(1 / 3) Φ(2 . 33) - Φ(0 . 33) = 0 . 9901 - 0 . 6293 = 0 . 3608 2. [Enhancing the Yield of Cell Phones] (a) As V A = 1 + IR and I = 10 - 3 , E [ V A ] = E [1 + IR ] = 1 + IE [ R ] = 1 + 10 - 3 × 10 3 = 2 V V ar [ V A ] = V ar [1 + IR ] = I 2 V ar [ R ] = 10 - 6 × 10 4 = 10 - 2 V 2 (b) As R has a N (1 k Ω , 10 4 Ω 2 ) distribution, V A has a

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## This note was uploaded on 02/09/2011 for the course ECE 313 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.

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Fall 2010 HW08 - University of Illinois Fall 2010 ECE 313:...

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