You are interested in monitoring the downside risk of your portfolio. suppose that unbeknownst to you the actual monthly return distribution of your portfolio is a mixture or normals similar to the example we discussed in class. we assume there is a bernoulli state variable, s, that defines whether the return is drawn from the market shock regime (s = 1) defined by random variable w or the regime covering standard market conditions (s = 0) represented by random variable v. as in class we assume all three variables are jointly independent and governed by the following