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Problem 3. In the setting of Problem 1, what is the expected value and the variance of the first ...

Problem 3. In the setting of Problem 1, what is the expected value and the variance of the first day when the stock price goes up? What is the MGF of this day? What is the probability that this day happens on the sixth day?

Problem 1. An investment analyst found that a certain stock price goes up or down a point every day with probabilities 0.75 and 0.25, respectively. Daily fluctuations are independent. Find the probability that after four days, the stock price will be the same as initially?

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