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:
There would be 12 gallons left
Step-by-step explanation:
If there was 76 of the 2 quarter pitchers that would make 152 Qt and 152 Qt equals 38 gallons so 50 - 38 = 12
Answer:
f(x) = x³ - 5x² - 9x + 45
Step-by-step explanation:
Given x = a, x = b are the zeros of a polynomial, then
(x - a), (x - b) are the factors and f(x) is the product of the factors.
Here the zeros are x = - 3, x = 3 and x = 5, thus
(x + 3), (x - 3) and (x - 5) are the factors and
f(x) = (x + 3)(x - 3)(x - 5) ← expand the first pair of factors using FOIL
= (x² - 9)(x - 5) ← distribute
= x³ - 5x² - 9x + 45
Answer:
I got -60
I'm pretty good at this.. oop guess I missed a step
