Lecture not 2

# 1 09 erfx 08 07 inverse is important in some

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Unformatted text preview: ion is monotonically decreasing, hence invertible. 1 0.9 erf(x) 0.8 0.7 • Inverse is important in some applications (signal detection). 0.6 Erfc: complementary error function ⁄ 0.5 0.4 erfc(x) 0.3 0.2 0.1 0 27 x 0 0.5 1 1.5 2 2.5 3 28 Erf and Gaussian Density Relation to Normal Distribution / Probability Less than Upper Bound is 0.9452 0.8 / 0.7 0.6 Normal Distribution: mean zero, variance 0.5 N Density 0.5 ⁄ 0.4 0.3 0.2 2. 0.1 0 -2 -1.5 -1 -0.5 0 0.5 Critical Value 1 1.5 x ⁄( × . ) For negative 2 3. use 29 MATLAB: Computing Probabilities (similar for Maple) 30 Example: Test Scores • Test scores are normally distributed with N >> erf(x) % Error function >> erfc(x) % Complementary error function >> 0.5*(1+erf(x/sqrt(2)) ) % St. Normal P (t < x) >> 0.5*erfc(x/sqrt(2)) % St. Normal P (t > x) >> Qinv=sqrt(2)*erfinv(1-2*P) % Inverse Q(P) 31 >> fun = @(x) exp(-(x-83).^2/128)./sqrt(128*pi); >> integral(fun,83-16,83+16) % within 2 sigma ans = 0.9545 32 Impulsive pdf Pseudorandom Number Generators f(y) >> rand % Uniform distribution over [0,1] >> randn % Standard normal Shifti...
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## This document was uploaded on 02/23/2014 for the course EE 782 at University of Nevada, Reno.

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