Unformatted text preview: 2. Let x ( n ) ∼ N (0 . 1 , . 0004) ⇔ E [ x ( n )] = 10% (historical average). 3. Con²dence limits or intervals (see pp. 275280 and recitation) are: Pr [8% < x ( n ) < 12%] = 67%; Pr [6% < x ( n ) < 14%] = 95%. 4. Let y ( n ) = p n i =1 (1+ x ( i )). Assume x ( n ) iidrvs. Then E [ y ( n )] = (1 . 1) n . 5. Generate 10 sample functions of x ( n ) (Matlab’s randn ) and y ( n ). Results plotted below. Curves are di±erent sample functions of y ( n ). • Note that the actual return can vary greatly from the expected return! So don’t plan on retiring too quickly! “Your performance may vary. ..” 10 20 30 40 20 40 60 #years invested since 2000 value of $1 invested...
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 Spring '10
 Lehman
 Probability theory, $1, 10%, 6%, 8%

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