Use the following outline to show that the binomial distribution tends to become gaussian distribution for...

 

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Use the following outline to show that the binomial distribution tends to become gaussian distribution for large sizes. N! q = No. of heads, N = No. of coins. n(q, n) = %3D q!(N-q)! Take the In (N) and use the Stirling's approx. In(n!) =n In(n) - n. Now focus on the distribution in the range close to the mean (q) = q0 = N/2 by rescaling q = qo + x, where x «N. Use the approximation In(1 + x) = x, for x «1 and show that !3! 2x2 N~2Ne n Comparing it with the standard form of gaussian, show that -13 Use the following outline to show that the binomial distribution tends to become gaussian distribution for large sizes. N! q = No. of heads, N = No. of coins. n(q, n) = %3D q!(N-q)! Take the In (N) and use the Stirling's approx. In(n!) =n In(n) - n. Now focus on the distribution in the range close to the mean (q) = q0 = N/2 by rescaling q = qo + x, where x «N. Use the approximation In(1 + x) = x, for x «1 and show that !3! 2x2 N~2Ne n Comparing it with the standard form of gaussian, show that -13

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We have given 2 C4 N q N9 In of both side we ... View the full answer