(Solved): 5. Sisters Andrea and Alexandra Botez are chess players with a modest online following. According ...

5. Sisters Andrea and Alexandra Botez are chess players with a modest online following. According to chess.com, Andrea has a very respectable 1800 rating while Alexandra has an even stronger 2100 rating. Based upon these ratings and your own skill at chess, you estimate the following probabilities of success against either player: You sign up for a match and only see your opponent listed as "A. Botez", so you don't know which sister you are playing. Define the following random variables. Let $$Y=1$$ if you win, $$Y=1/2$$ if you draw, and $$Y=0$$ if you lose. Further, let $$?=1$$ if you play Andrea and $$?=0$$ if you play Alexandra. Assume before you play you have an equal probability of facing off against either sister. 1 a. Name the prior distribution of $$?$$ and give its expected value. What does this expected value mean in terms of the problem? b. Give the marginal distribution of $$Y$$ and its expected value. What does this expected value mean in terms of the problem? c. Give the posterior distribution $$p(??Y=1)$$. Explain what the distribution means in the context of the problem.