According to the National Bureau of Economic Research (NBER), since 1945 to 2009 (extremes included) there has been approximately 11 business cycles. Assume that on average contractions (c) last 10.24 months while expansions last 53.76 months and define normal times (n) as 60% of the expansion months, characterizing the residual months as booms (b). Furthermore, suppose the expected return on the US market conditional on contractions to be 17%, i.e. M(c) = 0.17, during normal times to be 1%, and overall to be 8%. Characterize both analytically and graphically: A The probability distribution function (pdf) of the market return rM B The cumulative distribution function (cdf) of the market return rM Lets now assume the market return to be a continuous random variable, normally distributed with expected value M = 0.08 and variance 2 M C Compute the variance 2 M assuming is the same as the one from the discrete distribution