Shreve II Problems Sheet
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Problems Sheet
Revision Questions These questions relate to the maths that (I think) you already know. If not, don’t worry - have another look at the Prerequisites document. Exercise 0.1 Suppose \(X \sim \cN(\mu, \sigma^2)\) and \(Y = a + bX\) (\(b \neq 0\)). Find \(\E(Y)\), \(\Var(Y)\) and \(\Cov(X, Y)\). What is the distribution of \(Y\)? Exercise 0.2 In each round of a game you win \(0.15\) with chance \(0.55\) or lose \(0.1\) with chance \(0.45\). Successive rounds are independent and you play 1,000 times. Use the Central Limit Theorem to estimate the chance that your total winnings exceed 35.…
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