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5. Show that [² -1 (k+ 1)²¹ where k> -1 using the gamma function. Hint: consider the substitution u-logx. x log x dx =

5. Show that [² -1 (k+ 1)²¹ where k> -1 using the gamma function. Hint: consider the substitution u-logx. x log x dx =

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5. Show that -1 (k+ 1)²¹ where k> -1 using the gamma function. Hint: consider the substitution u = -logx. S² xk 6. The Poisson Distribution is given by W Pn = H log x dx = where μ > 0 is the mean and Enopn Gamma function for large z is n=0 Q Search μne μ n! T(+1)≈ √2 2²+1/2e-². Use this approximation to show that the Poisson Distribution becomes a Gaussian Distribution when u > 1 and n » 1, i.e., that Pn ≈ - 1. The Stirling approximation for the e-(n-μ)²/(2μ) 12πμ K
Transcribed Image Text:5. Show that -1 (k+ 1)²¹ where k> -1 using the gamma function. Hint: consider the substitution u = -logx. S² xk 6. The Poisson Distribution is given by W Pn = H log x dx = where μ > 0 is the mean and Enopn Gamma function for large z is n=0 Q Search μne μ n! T(+1)≈ √2 2²+1/2e-². Use this approximation to show that the Poisson Distribution becomes a Gaussian Distribution when u > 1 and n » 1, i.e., that Pn ≈ - 1. The Stirling approximation for the e-(n-μ)²/(2μ) 12πμ K
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