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. fu(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 a B The cumulative distribution function (cdf) of the market return FM hint: first compute the probabilities of the states of the world, then check if you have all the associated expected returns (if not calculate the missing one(s)), finally refer back to the notes where we introduced the pdf and edf for discrete random returns Let's now assume the market return to be a continuous random variable, normally distributed with expected value um = 0.08 and variance o C Compute the variance a assuming is the same as the one from the discrete distribution D For the following realizations of im {ru) = m + ion}-.-3.34 1. compute, using the excel function NORMDIST("C). Am.OM.0), the normal pdf (rur(i)) and draw its graph 2. compute, using the excel function NORMDIST( TCC). Mas, 0, 1), the normal edf (r-()) and draw its graph hint: I am not asking you to draw the graphs with Excel, you can if you know how, you can simply use a pen and a paper. E Compute the following probabilities: 1. Problem - 20M Simi) Sun + 20M) 2. Probrn(i)