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A directed graph is simple if each ordered pair of vertices is the head and tail of at most one edge; one loop may be present at each vertex. For each n ≥ 1, prove or disprove the following statement. Every simple directed graph with n vertices has two vertices with the same outdegree or two vertices with the same indegree.
(a) How many words of length 2 are there over the alphabet A = { 0; 1; 2; 3}?
(b) Construct the de Bruijn digraph D4,2 and use this digraph to nd an appropriate de Bruijn sequence.
(c) For b = 4 and n = 2, how many de Bruijn sequences can be formed?
Suppose [S, T] and [X, Y ] are two minimal cuts in a network N. Prove that both [S [X U T ∩ Y ] and [S ∩ X, T U Y ] are also minimal cuts in N.
Bayesian confidence interval : An interval of the posterior distribution which is so that the density of it at any point inside the interval is greater than that of the density at
Bayesian inference : An approach to the inference based largely on Bayes' Theorem and comprising of the below stated principal steps: (1) Obtain the likelihood, f x q describing
Can I use ICC for this kind of data? Wind Month Day Temp(DV) 7.4 5 1 67 8 5 2 72 12.6 5 3 74 11.5 5 4 62 I am taking temp as the dependent variable. There are many more values.
Principal components regression analysis is a process often taken in use to overcome the problem of multicollinearity in the regression, when simply deleting a number of the expla
Catastrophe theory : A theory of how little is the continuous changes in the independent variables which can have unexpected, discontinuous effects on the dependent variables. Exam
Multivariate analysis of variance is the procedure for testing equality of the mean vectors of more than two populations for the multivariate response variable. The method is dire
Healthy worker effect : The occurrence whereby employed individuals tend to have lower mortality rates than those who are unemployed. The effect, which can pose the serious problem
Multivariate data is the data for which each observation consists of the values for more than one random variable. For instance, measurements on the blood pressure, temperature an
Model is the description of the supposed structure of a set of observations which can range from a fairly imprecise verbal account to, more commonly, a formalized mathematical exp
The problem that the studies are not uniformly probable to be published in the scientific journals. There is evidence that the statistical significance is a main determining factor
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