Assume that the initial means and variances of two clusters in a GMM are as follows: μ(1)=−3 , μ(2)=2 , σ21=σ22=4 . Let p1=p2=0.5 . Let x(1)=0.2 , x(2)=−0.9 , x(3)=−1 , x(4)=1.2 , x(5)=1.8 be five points that we wish to cluster. In this problem and in the next, we compute the updated parameters corresponding to cluster 1. You may use any computational tool at your disposal. Compute the following posterior probabilities (provide at least five decimal digits):

1) p(1|1)
2) p(1|2)
3) p(1|3)
4) p(1|4)
5) p(1|5)

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed