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:
If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then ab is an irrational number lying between a and b.
So an irrational number between 3 and 4 is=3×4=3×4=3×2=23
Answer:
Step-by-step explanation:
Since this is not factorable, let's just complete the square:
Answer:
342 inches, or 28.5 feet, or 9.5 yards
Step-by-step explanation:
It is perhaps easiest to start with all the dimensions in inches.
13.5 ft = (13.5 ft)(12 in/ft) = 162 in
3.5 yd = (3.5 yd)(36 in/yd) = 126 in
Then the total of the lengths of ribbon is ...
54 in + 162 in + 126 in = 342 in
Converting to feet, we get ...
(342 in)/(12 in/ft) = 28.5 ft
And converting to yards, we get ...
(342 in)/(36 in/yd) = 9.5 yd
The total length of ribbon is 342 inches, or 28.5 feet, or 9.5 yards.
Hello!
To solve, we want to isolate the x on one side of the equation. We can use inverse operations to put numbers on the other side to find x.
First we undistribute our parentheses.
12x-66+15=21
We subtract 15 from both sides (it cancels out the 15 on the left side, making it 0).
12x-66=6
Now we add 66 to both sides, as -66+66=0
12x=72
Finally, we divide both sides by 12.
x=6
I hope this helps!
