Question: a) The probability density function of the Gaussian distribution is given by px; , 2) = (2)4/2/2/(x-)-1(x-) Explain what each symbol denotes and give

a) The probability density function of the Gaussian distribution is given by

px; , 2) = (2)4/2/2/(x-)-1(x-) Explain what each symbol denotes and give

a) The probability density function of the Gaussian distribution is given by px; , 2) = (2)4/2/2/(x-)-1(x-) Explain what each symbol denotes and give its dimensionality. Sketch the probability density function in the 1-dimensional case and use it to support your explanations. [8 marks] b) Fit a Gaussian distribution to the following set of 1-dimensional data X = (3,2,1,1,2,3). Show the formulas that you use for your estimation and state what is the criterion that is optimised. [10 marks] c) In several cases the covariance matrix is singular and cannot be inverted. In which cases is this more likely to happen? Why is this a problem? Give a solution to it. [7 marks]

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