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Q4) Define the events uA=Up-A, UB=Up-B, and uC=Up-C, each indicating if the respective daily stock price has gone up or not relative to yesterday

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Q4) Define the events uA=Up-A, UB=Up-B, and uC=Up-C, each indicating if the respective daily stock price has gone up or not relative to yesterday. 1) Obtain a two-way contingency table between uA and uB. 2) Compute P(UA),P(UB), P(UAN UB),P(UA U UB), P(UA|UB), P(UB|UA),P(UAC |UBC), P(UBC \UA). 3) Investigate if uA and uB are independent. 4) Investigate if uA and uB are independent conditional on uC. Q5. 1) Obtain the histograms for the daily returns of A, B, and C on the same plot. Add a vertical line to each plot for the respective means. 2) Compute the probability that each will yield a daily positive return. 3) Assume that you have $1 to invest in 3 stocks (A, B, and C) and assume that you would like to invest 30% in A, 35% in B, and 35% in C. Compute the expected return and the standard deviation of this portfolio and compare these measures against those obtained with A, B, and C individually. Briefly comment on your findings.