Unformatted text preview: the amounts paid o² the principal do add up to L . 3. Suppose X ∼ N ( μ, σ 2 ) and Y = a + bX ( b n = 0). ±ind E ( Y ), Var( Y ) and Cov( X, Y ). What is the distribution of Y ? ±ind E ( e X ). 4. 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. 5. Suppose that over a unit period the price of a stock changes from s to either us with chance p or ds with chance 1 − p . Successive price changes are independent. Estimate the probability that the stock price will increase by at least 30% over the next 100 time periods when u = 1 . 02, d = 0 . 98 and p = 0 . 52. Hint: switch to log scale and compare with the previous problem. 1...
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 Spring '10
 DrI.M.MacPhee
 Math, Remainder, Central Limit Theorem, Credit card, Logarithmic scale, Logarithm

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