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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.
Recursive models are the statistical models in which the causality flows in one direction, that is models which include only unidirectional effects. Such type of models do not inc
This is given by common network e.g. Phone Company. The public networks are those networks, which are given by common carriers. It can be a telephone company or an other organizati
The method or technique for displaying the relationships between categorical variables in a type of the scatter plot diagram. For two this type of variables displayed in the form o
Grade of membership model: This is the general distribution free method for the clustering of the multivariate data in which only categorical variables are included. The model ass
we are testing : Ho: µ=40 versus Ha: µ>40 (a= 0.01) Suppose that the test statistic is z0=2.75 based on a sample size of n=25. Assume that data are normal with mean mu and standa
There is high level of fluctuation in a zigzag pattern in the time series for RESI1 which indicates that there is possibly negative autocorrelation present. Column C11 show
Over dispersion is the phenomenon which occurs when empirical variance in the data exceeds the nominal variance under some supposed model. Most often encountered when the modeling
The Null Hypothesis - H0: Model does not fit the data i.e. all slopes are equal to zero β 1 =β 2 =...=β k = 0 The Alternative Hypothesis - H1: Model does fit the data i.e. at
Models for the analysis of the survival times, or the time to event, data in which it is expected that a fraction of the subjects will not experience the event of interest. In a cl
Paired availability design is a design which can lessen selection bias in the situations where it is not possible to use random allocation of the subjects to treatments. The desig
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