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F} is not considered a parameter since it must be selected in advance, based on what you want the range to be. You recognize a single-parameter Pareto by its having support not starting at 0, and by the density function having a denominator with x raised to a power. A beta distribution may also have x raised to a negative power, but it would have finite support. A single-parameter Pareto X is a two-parameter Pareto Y shifted by fJ: X = Y + f}. Thus it has the same variance, and the mean is f} greater than the mean of a two-parameter Pareto with the same parameters.

Xji from each and divide by 5, but since we're just comparing A and B, we won't bother subtracting xji. 21. 98 Thus either 96 or 97 experiments are needed. 4j. (A) An alternative to calculus that is more appropriate for this discrete problem is to note that as n increases, at first expected profit goes up and then it goes down. Let Xn be the expected profit with n experiments. 98n)- 2900. 98, a negative number. 582, or n:::; 96, the same conclusion as above. C/4 Study Manual-! 22. Since the median is 800, ell= 800 and J1.

5. 5 and a = 2. 8438 2 I D EXAMPLE 2C Claim sizes X initially follow a distribution with density function: rx Fx(x)=1--- l+x x>O Claim sizes are inflated by 50% uniformly. Calculate the probability that a claim will be for 60 or less after inflation. ANswER: Let Y be the increased claim size. 5) = Fx(40). 2 D Transformations When this material was tested separately by the CAS as part of Exam 4B (before 2000) or Exam 3 (2003-2006), they occasionally asked questions requesting a transformation of a random variable.

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