20. Probability-wreighted means and stsndard deviations The previous section discussed calculating descriptive statistics using "ex post" (histerical) data. This mechod is effective for deseribing past events. fit addition, you can ube histoncal resuits to characteride future events-that in, if you can reasonably assume that fubure Events will resemble past civents. Howevec, if a religbie Brobeblity distribution is avalable, you can calculate expected descrictive stacistics (also called "ex ante" subeisbes). The probabilty distribution describes all the possible outconves a variable cas aswurne. Using probabilty data, you cas calculate the espected mean, variance, and standard deviation uting the feilewing formulas =i=1pixia3=i=1P(xi)3=i A probablity distribution for five poswble market condions is whom below, along mith the eapected demand in each state. Caiculate the expected value (meien) and itandard deviatien ef demand A probsbiliy distribution for five possible market conditions is shown belew, along wah the expected demand in each state. Caloulate the expected value (mean) and standard deviation of demand. If you ignored the probasilay weghts and aswumed the market conetiens were egualy probable, the mean demind wevild be 3s, ooo unts and the standard deviation would be 25,100 units. Using the probability weghts, calculate the folioning statistics Expected mean = sumeard deviation =