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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.
This term is sometimes used for the analysis of data from the clinical trial in which treatments A and B are to be compared under the suppositions that the patients remain on their
Hello , I have a business statistic HW that is due after 23 hours exactly for now . I need full and details answers please , plus they must be in a done and typed in a word or exce
The analysis of data which are the functions observed continuously, for instance, functions of time. Basically a collection of statistical techniques or methods for answering quest
Cointegration : The vector of not motionless time sequence is said to be cointegrated if the linear combination of the individual series is stationary. Facilitates suitable testing
Group visible design is an arrangement of the v mn treatments in b blocks such that: * Each block comprises k distinct treatments k5v; * Each treatment is replicated r number
Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten
Blinder Oaxaca method: A method or technique used for assessing the effect of the role of income on racial wealth gap. The method or technique is based on the decomposition of the
Range is the difference between the largest and smallest observations in the data set. Commonly used as an easy-to-calculate measure of the dispersion in the set of observations b
Computer-assisted interviews : A method or technique of interviewing subjects in which the interviewer reads the question from the computer screen instead of the printed page, and
Indirect standardization is the procedure of adjusting the crude mortality or morbidity rate for one or more variables by making use of a known reference population. It may, for in
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