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# PS1 - (b Compute its expectation(c Compute the expectation...

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Economics/Mathematics C103: Introduction to Mathematical Economics Problem Set 1 Due 17 January 2009 1. Consider the exponential distribution F ( x ) = 1 - exp( - λx ). Assume ω = . (a) Compute the probability density function. (b) Compute its expectation. (The answer is in the book, but of course you are expected to prove why.) (c) Compute the expectation of γ ( x ) = x 2 . (d) Compute its hazard ratio. (e) Compute the conditional expectation E [ X | X < x ]. 2. Consider the uniform distribution F ( x ) = x/ω on [0 ]. for some arbitrary ω . (a) Compute the probability density function.
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Unformatted text preview: (b) Compute its expectation. (c) Compute the expectation of γ ( x ) = x 2 . (d) Compute its hazard ratio. (e) Compute the conditional expectation E [ X | X < x ]. Discussion questions Jan 22 Three roommates lease a furnished 3 bedroom apartment for \$2000 a month. The rooms diﬀer in size, furniture, paint color, windows, etc. How would you decide which roommate gets which room and how much each should pay? Jan 27 Bring some cash in small bills. We will auction some real items in class. 1...
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