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)