1.2) "Apple" and "Microsoft", both leading companies in the tech industry, adjust their financial strategies in reaction to fluctuations in specific macroeconomic variables. These variables can include, inter alia, interest rates, which can impact their investments and borrowing decisions. In this context, we use A to represent Apple's adaptation to these signals. Here, a=0 indicates no significant adjustment to the economic signal, a=1 represents a moderate adjustment and a=2 signifies a major strategic shift. Similarly, for Microsoft, we denote their adaptation using M, with m taking values 0,1 , or 2 following the same criteria. The table below presents the joint distribution of adaptation levels for both Apple and Microsoft. Table 1: Joint Distribution of Adaptation Levels for Apple and Microsoft (a) Calculate the marginal probability mass function of Apple's adaptation level, A. (b) Calculate the expected value and the variance of Apple's adaptation level, A. (c) Are the adaptation levels of the two companies to macroeconomic signals statistically independent? (d) Given that Microsoft has made a moderate adaptation (m=1), calculate the probability that Apple makes a similar moderate adaptation (a=1) in reaction to the same macroeconomic signals. (e) Calculate the conditional expectation of Apple's adaptation level given that Microsoft has made a major adaptation shift (m=2)