W - 6/5 = -2
w - 6 = -2 x 5 = -10
w = -10 + 6
w = -4
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:
A. 24 ≤ a < 26.
B. 22.5
Step-by-step explanation:
A. Determination of the modal class interval.
Mode is the class with the highest frequency.
From the table given above, the highest frequency is 8, therefore the class will the highest frequency is:
24 ≤ a < 26.
B. To obtain the mean, we must determine the class mark. This is illustrated below:
Class >>>>> class mark >>> frequency
18 – 19 >>>> 18.5 >>>>>>>>> 3
20 – 21 >>> 20.5 >>>>>>>> 2
22 – 23 >>> 22.5 >>>>>>>> 7
24 – 25 >>> 24.5 >>>>>>>> 8
26 >>>>>>>> 26 >>>>>>>>> 0
The mean is given by the summation of the product of the class mark and frequency divided by the total frequency. This is illustrated below:
Mean = [(18.5x3) + (20.5x2) + (22.5x7) + (24.5x8) + (26x0)] / (3+2+7+8+0)
Mean = (55.5 + 41 + 157.5 + 196 + 0)/20
Mean = 450/20
Mean = 22.5
Therefore, the mean age is 22.5
