Assignment_2 - STAT 230 Assignment 2 Due in class on Friday...

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STAT 230 - Assignment 2 Due in class on Friday November 12 1. Suppose X is a random variable with probability function f x kx 0.3 x 1 , x 1,2, a Given that f x is a probability function, find k . b Find E X . Hint: Since 1 t t 2 t 3 x 0 t x 1 1 t , | t | 1 by the Binomial series then by the theorem on the differentiation of power series d dt x 0 t x d dt 1 1 t , | t | 1. 2. The number of earthquakes of magnitude 7 or greater per year world-wide during the years 1990 2009 (see http://earthquake.usgs.gov/earthquakes/eqarchives/year/) is given below. For convenience we refer to these earthquakes as M7 earthquakes. The average number of M7 earthquakes per year based on these data is 297/20 14.85. Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Number of Earthquakes 18 16 13 12 13 20 15 16 12 12 Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Number of Earthquakes 15 16 13 15 16 11 11 18 12 17 Suppose it is assumed that the number of M7 earthquakes in a year follows a Poisson process with intensity, , measured in earthquakes per year. a What three assumptions does this make about the occurrences of earthquakes? How likely is each of the assumptions? For the following questions you may assume that
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Assignment_2 - STAT 230 Assignment 2 Due in class on Friday...

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