You are a coin trader. You have $1,000,000, and today one coin costs $2000. Tomorrow the coin will either cost $1000 or $4000, each with equal probability. Assume the prices are constant all day and change instantly at midnight. For each of the following, give a strategy and why it’s correct: (a) If you want to maximize the expected amount of money you have tomorrow, what should you do? (b) If you want to maximize the expected number of coins you have tomorrow, what should you do?

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