For a successful implementation of Q5-Q11 in the mini-project it is important that you get the model right in Q1-Q3. This quiz is to verify that your model is correct by considering the three distributions asked for in Q3. If you don't get this right, try to find your error. If you don't find it, ask for help. Do not proceed with the project before you via this quiz have confirmed your model.

First, derive closed for expressions for the three distributions asked for in Q3. Then, for this quiz only, plug in the values based on the following information

Consider the prior of the skill of Player 1 $LaTeX: p\left(s_1\right)$ to have mean 1 and variance 1.
Consider the prior of the skill of Player 2 $LaTeX: p\left(s_2\right)$ to have mean -1 and variance 4.
Consider the likelihood for the outcome of a match given the two skills to have variance 5.