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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.
1. You are interested in investigating if being above or below the median income (medloinc) impacts ACT means (act94) for schools. Complete the necessary steps to examine univariat
The values assigned to factors for the individual sample units in a factor analysis. The most common approach is "regression method". When the factors are seen as the random variab
Multiple correlation coefficient is the correlation among the observed values of dependent variable in the multiple regression, and the values predicted by estimated regression
Auto correlation : The correlation of the internal observations in the time series, generally expressed as a function of the time lag between the observations. It is also used for
The measure of the degree to which the particular model differs from the saturated model for the data set. Explicitly in terms of the likelihoods of the two models can be defined a
Machine learning is a term which literally means the ability of a machine to recognize patterns which have occurred repetitively and to improve its performance based on the past
Lorenz curve : Essentially the graphical representation of cumulative distribution of the variable, most often used for the income. If the risks of disease are not monotonically in
The model which is applicable to the longitudinal data in which the dropout process might give rise to the informative lost values. Specifically if the study protocol specifies the
ain why the simulated result doesn''t have to be exact as the theoretical calculation
An investor with a stock portfolio sued his broker, claiming that a lack of diversification in his portfolio had led to poor performance. The data, shown below, are the rates of re
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