1) [5 pts] Take the binomial coefficient CN,k= for N = 10 and N = 20,...

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1) [5 pts] Take the binomial coefficient CN,k= for N = 10 and N = 20, and make a plot where CN.k 2N √N is the vertical axis, and N! k!(N-k)! 2.8 2k - N VN (1) N k=0 (N-ky! (2k-N)¹ 2N (2) (3) is the horizontal axis. You might find it useful do this using a computer. If you can, try also N = 100. Explain why CNA and y were scaled this way, and explain the value that this plot is converging to in the large N limit at y = 0. 2) [5pts] Compute ((2s))= (4) exactly as a function of N, and compare to the expectation based on Gaussian limit of the binomial coefficient for large N. 1) [5 pts] Take the binomial coefficient CN,k= for N = 10 and N = 20, and make a plot where CN.k 2N √N is the vertical axis, and N! k!(N-k)! 2.8 2k - N VN (1) N k=0 (N-ky! (2k-N)¹ 2N (2) (3) is the horizontal axis. You might find it useful do this using a computer. If you can, try also N = 100. Explain why CNA and y were scaled this way, and explain the value that this plot is converging to in the large N limit at y = 0. 2) [5pts] Compute ((2s))= (4) exactly as a function of N, and compare to the expectation based on Gaussian limit of the binomial coefficient for large N.