<jupyter_start><jupyter_text>N = 5<jupyter_code>n = 5

plt.hist(f(n, 1000), bins=20, normed=True, label='sample')
plt.ylabel('fraction of samples')
plt.xlabel('$x$')

norm_rv = sts.norm(mean, sqrt(variance / n))
x = np.linspace(0, 6, 100)
pdf = norm_rv.pdf(x)

plt.plot(x, pdf, color='r', label='theoretical PDF')
plt.legend()<jupyter_output><empty_output><jupyter_text>N = 10<jupyter_code>n = 10

plt.hist(f(n, 1000), bins=20, normed=True, label='sample')
plt.ylabel('fraction of samples')
plt.xlabel('$x$')

norm_rv = sts.norm(mean, sqrt(variance / n))
x = np.linspace(0, 6, 100)
pdf = norm_rv.pdf(x)

plt.plot(x, pdf, color='r', label='theoretical PDF')
plt.legend()<jupyter_output><empty_output><jupyter_text>N = 50<jupyter_code>n = 50

plt.hist(f(n, 1000), bins=20, normed=True, label='sample')
plt.ylabel('fraction of samples')
plt.xlabel('$x$')

norm_rv = sts.norm(mean, sqrt(variance / n))
x = np.linspace(0, 6, 100)
pdf = norm_rv.pdf(x)

plt.plot(x, pdf, color='r', label='theoretical PDF')
plt.legend()<jupyter_output><empty_output>
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{'chain_length': '3', 'dir': 'jupyter-structured-clean-dedup', 'id': '375747', 'license': 'MIT', 'n_tokens_mistral': 520, 'n_tokens_neox': 455, 'n_words': 82, 'path': 'data-science-course/course1/week5/final-test.ipynb', 'repo_name': 'yaskovdev/data-science-sandbox', 'size': '1042'}