1. Introduction. This paper discusses a special form of positive dependence.
Positive dependence may refer to two random variables that have
a positive covariance, but other definitions of positive dependence have
been proposed as well; see [24] for an overview. Random variables X =
(X1, . . . , Xd) are said to be associated if cov{f(X), g(X)} ≥ 0 for any
two non-decreasing functions f and g for which E|f(X)|, E|g(X)|, and
E|f(X)g(X)| all exist [13]. This notion has important applications in probability
theory and statistical physics; see, for example, [28, 29].
However, association may be difficult to verify in a specific context. The
celebrated FKG theorem, formulated by Fortuin, Kasteleyn, and Ginibre in
[14], introduces an alternative notion and establishes that X are associated if
∗
SF was supported in part by an NSERC Discovery Research Grant, KS by grant
#FA9550-12-1-0392 from the U.S. Air Force Office of Scientific Research (AFOSR) and
the Defense Advanced Research Projects Agency (DARPA), CU by the Austrian Science
Fund (FWF) Y 903-N35, and PZ by the European Union Seventh Framework Programme
PIOF-GA-2011-300975.
MSC 2010 subject classifications: Primary 60E15, 62H99; secondary 15B48
Keywords and phrases: Association, concentration graph, conditional Gaussian distribution,
faithfulness, graphical models, log-linear interactions, Markov property, positive
So to find the mean you add them all together and divide by the number of numbers there is so 11+15+19+17+23+20+17+18+21=174 and there are 10 numbers so it would be 174/10 which is 17.4 so you answer is 17.4
Answer:
A: (-9,-3)(-2,-4)(-5,-8)
B: (-5,2)(-1,-3)(3,2)
C: (4,-7)(-1,-3)(4,1)
D: (-1,-11)(-2,-4)(-6,-7)
Step-by-step explanation:
So of the transformations, translations are pretty much the easiest. x-1 just means move all coordinates left 1 and y-3 means move all coordinates down 3. So for the first one the x coordinate gets 1 subtracted from it and the y value gets 3 subtracted from it.
(-8,0) => (-8-1, 0-3) = (-9,-3)
I do recommend double checking though, for practice and in case I flubbed a calculation.
Answer:
<em>Hope</em><em> </em><em>this is</em><em> </em><em>correct</em><em> </em>
Step-by-step explanation:
HAVE A GOOD DAY!
