Consider the bi-variate Gaussian random vector [X Y] similarity N ([1 0], [1 1.6

Question

Consider the bi-variate Gaussian random vector [X Y] similarity N ([1 0], [1 1.6 1.6 4]) Generate N = 1000 random samples of [X, Y]^T. Generate a scatter-plot of your samples, i.e., for each realization i, plot the sample point (x_i, y_i) with a dot. Use your samples to (approximately) compute the probability P[1 less than or equal to X less than or equal to 3, 2 less than or equal to Y less than or equal to 4]. Do this by reporting the fraction of sample points that fall within the region of interest.

Explanation / Answer

Consider the bi-variate Gaussian random vector [X Y] similarity N ([1 0], [1 1.6

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