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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.
Link functions: The link function relates the linear predictor ηi to the expected value of the data. In classical linear models the mean and the linear predictor are identical
Law of likelihood : Within framework of the statistical model, a particular set of data supports one statistical hypothesis or assumption better than another if the likelihood of t
Bartlett decomposition : The expression for the random matrix A which has a Wishart distribution as the product of the triangular matrix and the transpose of it. Letting each of x
An unusual aggregation of the health events, real or perceived. The events might be grouped in the particular region or in some short period of time, or they might happen among the
Multiple comparison tests : Procedures for detailed examination of the differences between a set of means, generally after a general hypothesis that they are all equal has been rej
The procedures for extracting the pattern in a series of observations when this is obscured by the noise. Basically any such technique or method separates the original series into
Histogram is the graphical representation of the set of observations in which class frequencies are represented by the regions of rectangles centred on the class interval. If the f
How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;
The generalization of the normal distribution used for the characterization of functions. It is known as a Gaussian process because it has Gaussian distributed finite dimensional m
The distribution over distributions in the sense that each draw from the process is itself the distribution. The name Dirichlet process or procedure is due to the fact that the ?ni
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