Question: 3. [12 points] Let S be a discrete random variable with the following pmf: _ 1/3, .9 = 1 (3) _ {2/3, .9 = 4.

3. [12 points] Let S be a discrete random variable with

3. [12 points] Let S be a discrete random variable with the following pmf: _ 1/3, .9 = 1 \"(3) _ {2/3, .9 = 4. Given S = s, we generate a continuous random variable X from the normal distribution with mean 0 and variance 0'2 = 3. That is, if S = 1, we have that X N N(0, 1). If S = 4, x ~ Mo, 4). Suppose we observe X = 3. What is the conditional pmf for S given this observation

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