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 worldwide 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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 Fall '10
 MichaelLa
 Probability, Variance, Probability theory, PROBABILITY FUNCTION, M7 earthquakes

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