# Question: Consider the family of linear Gaussian networks as illustrated

Consider the family of linear Gaussian networks, as illustrated.

a. In a two-variable network, let X1 he the parent of X2, let X1 have a Gaussian prior, and let P (X2, X1) be a linear Gaussian distribution. Show that the joint distribution P(X1, X2) is a multivariate Gaussian, and calculate its covariance matrix.

b. Prove by induction that the joint distribution for a general linear Gaussian network on X1..., Xn, is also a multivariate Gaussian.

a. In a two-variable network, let X1 he the parent of X2, let X1 have a Gaussian prior, and let P (X2, X1) be a linear Gaussian distribution. Show that the joint distribution P(X1, X2) is a multivariate Gaussian, and calculate its covariance matrix.

b. Prove by induction that the joint distribution for a general linear Gaussian network on X1..., Xn, is also a multivariate Gaussian.

## Answer to relevant Questions

The probit distribution defined, describes the probability distribution for a Boolean child, given a single continuous parent.a. How might the definition be extended to cover multiple continuous parents?b. How might it be ...Consider the query P (Rain│Sprinkler = true, Wet-Grass = true) in Figure (a) and how MCMC can answer it. a. How many states does the Markov chain have? b. Calculate the transition matrix Q containing q (y → ...Complete the missing step in the derivation of Equation (15.17), the first update step for the one-dimensional Kalman filter.In 1738, J. Bernoulli investigated the St. Petersburg paradox, which works as follows. You have the opportunity to play a game in which a fair coin is tossed repeatedly until it conies up heads. If the first heads appears on ...Modify and extend the Bayesian network code in the code repository to provide for creation and evaluation of decision networks and the calculation of information value.Post your question