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:
D
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x)
A translation of 3 units up → + 3 in the y- direction, that is add 3 to the y- coordinate, hence
(x, y) → (- y, x) → (- y, x+ 3) → D
8
5
8
5
hopefully its right i'm not good at this kind of stiff
Q + d = 100 so q = 100 - d
0.25q + 0.10d = 19
substitute q = 100 - d into 0.25q + 0.10d = 19
0.25q + 0.10d = 19
0.25(100 - d) + 0.10d = 19
25 - 0.25d + 0.10d = 19
-0.15d = -6
d = 40
q = 100 - 40 = 60
answer
Kitara has 60 quarters and 40 dimes
