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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) Has smartphones affected the consumer behavior? If so How ? And how is it going to change in future? 2) Forecasting of Mobile market (Time series analysis) 3) Comparison of fou
Chance events : According to the Cicero these are events which occurred or will occur in ways which are the uncertain-events which may happen, may not happen, or may happen in some
A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha
Last observation carried forward is a technique for replacing the observations of the patients who drop out of the clinical trial carried out over a time period. It consists of su
Likelihood is the probability of a set of observations provided the value of some parameter or the set of parameters. For instance, the likelihood of the random sample of n observ
Committees to monitor the accumulating data from the clinical trials. Such committees have chief responsibilities for ensuring the continuing safety of the trial participants, rele
A name sometimes given to the type of diagram generally used in meta-analysis, in which point estimates and confidence intervals are displayed for all the studies included in the a
Non-identified response is a term used to signify censored observations in survival data, which are not independent of the endpoint of the interest. Such observations can happen f
The equation linking the height and weight of the children between the ages of 5 and 13 and given as follows here w is the mean weight in kilograms and h the mean height in
This graph for Cross Correlation Function for RES1, RES1 shows that there is possibly negative autocorrelation as there are alternating spikes; also the first spike is negative whi
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