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Unformatted text preview: b. at most 60 were minted in Philadelphia. In each case write (a) an expression for the exact (binomial) probability; and (b) the numerical result of either the Poisson or normal approximation, as appropriate. 1 Problem 4. (6 points) The moment generating function of X is given by φ ( t ) = 1 1 + t 2 . a. Find the variance of X. b. Find the moment generating function of 2 X + Y if X and Y are independent, identically distributed. (Hint: to handle the factor of 2, write down the deﬁnition of the moment generating function of X and replace X by 2 X there.) Problem 5 (3 points) Assume that pro golfers’ scores are normally distributed with mean 70.5 and variance 4.3. After the ﬁrst day of play at a golf tournament the ﬁeld of 200 players will be downsized to 50 by cutting all those above a certain score. What is the highest cutoﬀ score that is likely to achieve this goal? 2...
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 Spring '08
 Staff
 Normal Distribution, Probability theory, probability density function, Philadelphia Mint, San Francisco Mint, Denver Mint

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