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
Answer:
Step-by-step explanation:
Volume= length × width × height.... Volume= 20 1/2 × 12 × 10 1/4..... Volume= 2521 1/2 cubic inches or 2521.5 cubic inches
Answer:
5088
Step-by-step explanation:
212*24=5088
Know that:
sin(β)=Opposite/Hypotenuse
Therefore:
sin(54)=x/10
Therefore:
x=10*sin(54)
x=8.1 (To the nearest tenth)
Answer:
<h2><u><em>
55°</em></u></h2>
Step-by-step explanation:
the sum of the interior angles of a triangles is 180°
so
180 = 75 + 50 + x
x = 180 - 75 - 50
x = 55°
-----------------------
check
55 + 75 + 50 = 180°
the answer is good
