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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.
K-means cluster analysis is the method of cluster analysis in which from an initial partition of observations into K clusters, each observation in turn is analysed and reassigned,
The Current status data arise in the survival analysis if the observations are limited to the indicators of whether or not the event of interest has happened at the time the sample
The results of a survey determined whether the age of a driver 21 years and older has any effect on the number of motor vehicle accidents in which he/she is involved. Question 1:
Computer-intensive methods : The statistical methods which require almost identical computations on the data repeated number of times. The term computer intensive is, certainly, a
Interior analysis is the term now and again applied to analysis carried out on the fitted model in regression problem. The basic target of such analyses is the identification of
The graphic representation of the alternatives in a decision making problem which summarizes all the possibilities foreseen by the decision maker. For instance, suppose we are give
Intercropping experiments are the experiments including growing two or more crops at same time on the same patch of land. The crops are not required to be planted nor harvested at
Clinical vs. statistical significance : The distinction among results in terms of their possible clinical importance rather than simply in terms of their statistical importance. Wi
Regression line drawn as y= c+ 1075x ,when x was2, and y was 239,given that y intercept was 11. Calculate the residual ?
Ascertainment bias : A feasible form of bias, particularly in the retrospective studies, which arises from the relationship between the exposure to the risk factor and the probabil
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