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a. (4p) In programming language Python generate n = 15000 samples of RV X with Student t-distribution with (a + 10) degrees of freedom and plot a figure of dependence of standard deviation estimator (using generated data) on the number of samples (on x axis is the number of samples which goes from 1 to n). b. (5p) In programming language Python generate N = 15000 samples of RV (estimator of mathematical expectation of the above t-distributed RV) where each sample of the estimator is calculated using = 50(a + 1) samples from the mentioned t-distribution. Plot the normalized histogram of the obtained samples of the mean () and plot, on the same figure, the PDF which RV should (approximately) have based on the central limit theorem. n a. (4p) In programming language Python generate n = 15000 samples of RV X with Student t-distribution with (a + 10) degrees of freedom and plot a figure of dependence of standard deviation estimator (using generated data) on the number of samples (on x axis is the number of samples which goes from 1 to n). b. (5p) In programming language Python generate N = 15000 samples of RV (estimator of mathematical expectation of the above t-distributed RV) where each sample of the estimator is calculated using = 50(a + 1) samples from the mentioned t-distribution. Plot the normalized histogram of the obtained samples of the mean () and plot, on the same figure, the PDF which RV should (approximately) have based on the central limit theorem. n