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:
7.127
Step-by-step explanation:
Hope this helps!
Answer:
Each glass of milk is 9 carbs.
Each snack bar is 19.7 carbs.
Step-by-step explanation:
1. I know that 2 glasses of milk with 3 snack bars is 78 carbs.
The next part of the sentence has two times the amount of milk with the same amount of snack bars for 96 carbs.
Now, I will find the difference in the amount of carbs.
96 - 78 = 18 carbs.
So two glasses of milk = 18 carbs.
18 ÷ 2 = 9 carbs
So, each glass of milk is 9 carbs.
2. Since we know this, we can subtract the amount of carbs from the glasses of milk from the total amount of carbs.
78 - 19 = 59
In the first scenario, there are 59 carbs per 3 snack bars.
To find the amount of each snack bar, divide 59 by 3.
59 ÷ 3 = 19.7 when rounded to the nearest tenth.
Therefore, each snack bar is 19.7 carbs.
9514 1404 393
Answer:
A) 504
B) 8
Step-by-step explanation:
The statement of proportionality can be written as the equation ...
m = kr²
Then we can find k from ...
k = m/r² = 14/2² = 7/2
That is, ...
m = (7/2)r²
__
Using this relation, we can find m for r=12:
m = (7/2)·12² = 7·72
m = 504 . . . for r = 12
__
And, we can use the same equation to solve for r when m=224.
224 = 7/2·r²
r² = 64
r = √64
r = 8 . . . for m = 224
