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In the question, we are asked to determine which of the contour plots (a), (b), (c), or (d) could represent the probability density function (PDF) of a multivariate Gaussian distribution with a given covariance matrix: Option (a): This contour plot is a narrow elliptical shape that is highly elongated, and the orientation seems to suggest a positive correlation. However, this contour is much too narrow to represent the covariance matrix. Given that the variance along the 𝑥 x-axis is 2.5 (which should cause significant spread), this plot doesn't match the required covariance structure. Option (b): The contours in this plot are concentric ellipses, indicating no significant correlation between the variables. This type of circular or nearly circular pattern implies independent or uncorrelated variables, which is not the case with the given covariance matrix (since there is a non-zero covariance of 0.5). Hence, this is not the correct choice. Option (c): This plot shows an elliptical sha

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