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What is the purpose of the corporation? This is one of the most controversial and perhaps one of the most important questions that we need to address in this course and that you will need to address as the next generation workforce leaders. Why is this the case? Well, because American CEOs have answered this in two different ways. From the 1940s through the '70s and '80s and into the 1990s, there was a broad view of the corporation that has now narrowed down to focus on maximizing shareholder value in the short run. Here's a quote from the CEO of Sonesta Hotels, Roger Sonnabend. He says, "Social responsibility and expanding profitability are not at odds with one another. Quite the contrary. They are two faces of the same coin." That view was shared by a lot of CEOs of his era-- best illustrated perhaps by graduates of this important institution called the Harvard Business School. The class of 1949 is known for producing an enormous number of CEOs tha...

The purpose of this segment is to give you a little bit of the bigger picture. We did discuss some inequalities, we did discuss convergence of the sample mean-- that's the weak law of large numbers-- and we did discuss a particular notion of convergence of random variables, convergence in probability. How far can we take those topics? Let's start with the issue of inequalities. Here, one would like to obtain bounds and approximations on tail probabilities that are better than the Markov and Cherbyshev inequalities that we have seen. This is indeed possible. For example, there is a so-called Chernoff bound that takes the following form. The Chernoff bound tells us that the probability that the sample mean is away from the true mean by at least a, where a is a positive number, this probability is bounded above by a function that falls exponentially with n and where the exponent depends on the particular number, a, that we are considering. But in any case, this term ...