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
L*w=area
(3x+21)*w=3x^2+33x+84
w=(3x^2+33x+84)/3x+21
(3(x+4)(x+7))/3(x+7)
w=x+4
Answer:
(10*5) - 2(pi(2.5)^2)
Step-by-step explanation:
First we find the area of the rectangle. This is (10*5) since the diameter of the circles is 5 (half of 10) which means that the width of the rectangle is 5, and that the length is 10.
We then find the area of the two circles. One circle can be found using the radius (2.5)(half of the diameter, 5). This gives us pi(2.5)^2 for one circle. We multiply this by two to account for both circles. Then we subtract that from the area of the rectangle to find out how much the area of the plastic is.
This gives us (10*5) - 2(pi(2.5)^2)
Answer:
15m
Step-by-step explanation:
1cm=3m
5cm is equal to 15m
