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02 . 01 ... 005 .. 4: Probability density function of three gamma distributions with mean 50 ( When a does not satisfy these conditions, the corresponding moments don't exist. 5 graphs three Pareto distributions, one with a< 1 and the other two with mean 50. 5 puts higher weight on small numbers than the other two, its mean is infinite; it puts higher weight on large numbers than the other two, and its graph eventually crosses the other two as x -----+ oo. fJ a must be positive. f} is not considered a parameter since it must be selected in advance, based on what you want the range to be.
Ll. [3-F01:37] For watches produced by a certain manufacturer: (i) Lifetimes follow a single-parameter Pareto distribution with a> 1 and B = 4. (ii) The expected lifetime of a watch is 8 years. Calculate the probability that the lifetime of a watch is at least 6 years. 67 Exercises continue on tile next page ... 16 1. 12. [4B-F99:29] (2 points) You are given the following: • A is a random variable with mean 5 and coefficient of variation 1. B is a random variable with mean 5 and coefficient of variation 1.
But on SOA-only and joint exams, they have never asked a question directly on the material in this section. It is important background, but I do not expect direct exam questions on it. x(g-I(y)) dy It is easy to obtain a corresponding result for g(x) a one-to-one monotonically decreasing function. EXAMPLE 2D X follows a two-parameter Pareto distribution with parameters a and (}. You are given Determine the distribution of Y. 2. j_)a () eY -l)r = 1- e-ay SoY's distribution is exponential with parameter()= 1/a.