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Warm-up Problems

Warm-up Problems. Random variable X equals 0 with probability 0.4, 4 with probability 0.5, and -10 with probability 0.1. What is E[X]? What is E[X | X ≤ 1]? N(2,4) is a normal random variable. What is E[3+N(2,4)]?

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Warm-up Problems

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  1. Warm-up Problems • Random variable X equals 0 with probability 0.4, 4 with probability 0.5, and -10 with probability 0.1. • What is E[X]? • What is E[X | X ≤ 1]? • N(2,4) is a normal random variable. What is E[3+N(2,4)]? • Suppose an HIV test gives a negative result for an HIV- individual 99% of the time. If 1% of the population is infected, how many false-positives will you have if you test 1000 people?

  2. Previous Approach • List alternatives • For each alternative • Describe cashflow stream • Calculate NPV • Choose alternative with largest NPV

  3. New Approach • List alternatives • For each alternative • Describe average cashflow stream • Calculate average NPV • Choose alternative with largest average NPV

  4. New Approach • List alternatives • For each alternative • List possible scenarios and their probabilities • Describe cashflow stream • Calculate NPV • Calculate E[NPV] • Choose alternative with largest E[NPV]

  5. Simulation Example:Mortgage Backed Security • Consider a pool of 100 extremely risky mortgages. Each mortgage has an independent 50% probability of defaulting. • If a mortgage defaults it creates losses U[20k,70k] for investors. • Suppose this pool of mortgages into 2 tranches (or slices). The equity slice absorbs the first $2.1m in losses, and the mezzanine slice, absorbs the rest.

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