Consider the Bayesian network in the figure below. Suppose Wis instantiated (i.e, given) for w. P(x,) = .1 P(y,|x,) = .6 P(y,\x,) = .2 P(z,|x,) = .7 P(z,|x,) = .1 Y т P(w,ly,) = .9 P(w,ly) = .3 P(t,|z,) = .8 P(t,|z,) = .1 What is the value of P(yI m)? Select one: O a. 0.486 O b.0.24 O c. 0.198 O d. 0.444
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- a. The general continuous-time random walk is defined by g_(ij)={[mu_(i)",",j=i-1","],[-(lambda_(i)+mu_(i))",",j=i","],[lambda_(i)",",j=i+1","],[0","," otherwise "]:} Write out the forward and backward equations. b. The continuous-time queue with infinite buffer can be obtained by modifying the general random walk in the preceding problem to include a barrier at the origin. Put g_(0j)={[-lambda_(0)",",j=0","],[lambda_(0)",",j=1","],[0","," otherwise ".]:} Find the stationary distribution assuming sum_(j=1)^(oo)((lambda_(0)cdotslambda_(j-1))/(mu_(1)cdotsmu_(j))) < oo. If lambda_(i)=lambda and mu_(i)=mu for all i, simplify the above condition to one involving only the relative values of lambda and mu. c. Repeat a and b assuming there is a boundary at j=N. Comments.need explicit calculation process, step by stepShow that there is no hamiltonian path in Cay ({(1,0),(0,1)}: Z3 +Z2) from (0,0) to (2,0).How is the Jacobian formulated?
- Consider the following network in a matching problem:The compatibilities are:Edge CompatibilityFP 1.5FQ 2.5GP 1GQ 2HR 51. Write down an LP which can be solved to give the best matching (i.e. max compatibility) betweennodes F , G, H and nodes P , Q, R. Provide two optimal solutions – one that is a BFS and one that isnot a BFS. (Let xXY be the flow through edge XY)2. Formulate the dual of the LP and solve for optimal solutionFind a Hamiltonian circuit in Cay({(1, 0), (0, 1)}:Z4 ⊕ Z6).Consider the linear model Yi = B0 + B1X1i + B2X2i + ui where ui is the error term and where E(ui|X1i,X2i) = 0, observations (Yi,X1i,X2i) are independent and identically distributed, 0 < E(Y4) < 1, 0 < 1i E(X14i) < 1, 0 < E(X24i) < 1 and where X2i = X12i. Are the OLS estimators Bˆ1 and Bˆ2 of the coe¢cients B1 and B2 unbiased and consistent? Explain.
- What is the simple random walk on integers? Does it always return to the origin if p = ½ ? if p ≠ ½?At which point should i place the receiver on this satelite?Assuming Get Food Now achieved 12,000 interactions, how many of these would have resulted in customer being less than satisfied with their first interaction?