Lecture not 2

# Mean square use fourier transform table to obtain it

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Unformatted text preview: Mean: • Fourier transform of pdf. Mean Square: • Use Fourier transform table to obtain it. • Used to obtain the moments for a given pdf. Variance: 19 20 Series Expansion and Moments Moment Generating Function _ • Laplace transform of pdf • Use 2-sided Laplace transform table. → 21 22 Series Expansion and Moments Normal or Gaussian Density • • • • Symmetric about the mean mx. )= (larger for sharper peak) Peak value (at Mode (most likely value) = mean Standard normal distribution, zero-mean, unit variance / → 23 24 Why is it important? Right Tail Probability • Probability of exceeding a given value. >> p = normspec([-Inf,1],0,1,'outside') • Complementary cumulative distribution. • Fits many physical phenomena. • Central limit theorem. • Completely described by mean and variance. Probability Greater than Upper Bound is 0.15866 0.4 / 0.35 0.3 • Independent uncorrelated. Density 0.25 x 0.2 0.15 =Prob. of false alarm. 0.1 0.05 0 -4 25 -3 -2 -1 0 Critical Value 1 2 3 26 4 Error Function Inverse • Erf : error funct...
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