Estimates of Parameters of GMM: The Expectation Maximization (EM) Algorithm We observe n data points x1,…,xn in Rd . We wish to maximize the GMM likelihood with respect to the parameter set θ={p1,…,pK,μ(1),…,μ(K),σ21,…,σ2K} . Maximizing the log-likelihood log(∏ni=1p(x(i)|θ)) is not tractable in the setting of GMMs. There is no closed-form solution to finding the parameter set θ that maximizes the likelihood. The EM algorithm is an iterative algorithm that finds a locally optimal solution θ^ to the GMM likelihood maximization problem.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.

The drive force for diffusion is 7 fick's first law can be used to solve the non-steady state diffusion. a)-true b)-false