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It does not matter how many hours exam will take. . Terms 2002-2022 – The Uni Tutor – Custom Essays. , zd = i for some i, but zd+1 =6        i.
(a) Derive the probability mass function Pr(X = k; r, p) of the negative binomial distribution.

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(c) Rewrite the multivariate Gaussian density in natural exponential family form with parameters J and h.getFullYear()) Sandiv Consultancy LLC. These people helped me OK. Show that the negative binomial is the marginal distribution over X where X ∼Poisson(µ) and µ ∼Gamma(r, (1 −p)/p), integrating over µ.

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Show that the joint distribution is a multivariate
Gaussian and find a closed form expression the precision matrix, J.
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yn = wTxn + εn; εn∼(0,β−1),
where w∈D is a vector of regression weights and β∈+ specifies the precision (inverse variance) of the errors εn.

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You will also get a payment link using which you can make the payment.n=1The difference between VAE’s and regular variational expectation-maximization is that we constrained the variational distribution q(z | x, φ) to be a parametric function of the data; for example, we considered,q(zn | xn, φ)= N              zn | µ(xn; φ), diag([σ12(xn; φ), . Write the log likelihood L(r, p).As a result, our professional stat lab experts provide errorless Pearson MyStatLab answers for students who are struggling to find time in solving MyStatLab statistics homework answers.What value of w maximizes the expected log joint probability? Describe an EM procedure to search for,w∗ = arg max p(w | {(xn, yn)}Nn=1, α, a, b)..