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Unformatted text preview: • Mean • Variance • Moment Generating Function 7 (b) Gamma • Probability Mass Function • Mean • Variance • Moment Generating Function 8 (c) Normal • Probability Mass Function • Mean • Variance • Moment Generating Function 9 (d) Beta • Probability Mass Function • Mean • Variance • Moment Generating Function 10 (e) Exponential • Probability Mass Function • Mean • Variance • Moment Generating Function 11 (f) Chisquare • Probability Mass Function • Mean • Variance • Moment Generating Function 12 3. Exponential Families A family of pdfs or pmfs is called an exponential family if it can be expressed as f ( x ) = h ( x ) c ( θ ) exp( k X i =1 w i ( θ ) t i ( x )) where h ( x ) , c ( θ ) ≥ 0, t i ( x ), independent of θ , and w i ( θ ), independent of x are realvalued functions. Examples • Binomial • Normal 13...
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 Spring '11
 Ho
 Statistics, Binomial, Normal Distribution, Probability theory, WI, Probability mass function, moment generating function, Hypergeometric

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