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a) How many parameters does a mixture of m Gaussians have?

b) Let x1, . . . , xn be n observations drawn from a mixture of m Gaussians. Write down the log-likelihood function. (Hint: it should involve two summations.)

c) Let 1 ≤ k ≤ m. Show that the maximum likelihood estimator for µk is given b

and d)
A mixture of m univariate Gaussians has the PDF TIL where each P3 > 0 and Σ-1 pi-| , and N(x; μ, σ2)-(2πσ2)-1 /2 exp (-(z-p?/(2oY) a) How many parameters does a mixture of m Gaussians have? b) Let x1, ,In be n observations drawn from a mixture of m Gaussians. Write down the log-likelihood function. Hint: it should involve two summations. c) Let 1 k m. Show that the maximunn likelihood estimator for 쌔 is given by 7L ki where d) Let 1 k m. Show that the maximum! likelihood estimator for σ, is given by rL where Ykei is as defined above
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Please help a) How many parameters does a mixture of m Gaussians have? b) Let x1,...
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