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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Let X1, X2,... be the annual rainfalls in Boston (measured in inches) in the years 2101, 2102, . . . , respectively. Assume that annual rainfalls are i.i.d. draws from a continuous distribution. A rainfall value is a record high if it is greater than those in all previous years (starting with 2101), and a record low if it is lower than those in all previous years.
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(a) In the 22nd century (the years 2101 through 2200, inclusive), find the expected number of years that have either a record low or a record high rainfall.
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(b) On average, in how many years in the 22nd century is there a record low followed in the next year by a record high?
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(c) By definition, the year 2101 is a record high (and record low). Let N be the number of years required to get a new record high. Find P(N>n) for all positive integers n, and use this to find the PMF of N.
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