A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).
In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.
If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______
Consider the following expression
$$\mathop {\lim }\limits_{x \to -3} \frac{{\sqrt {2x + 22} - 4}}{{x + 3}}$$
The value of the above expression (rounded to 2 decimal places) is ______
Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:
diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and v}
Let M be the adjacency matrix of G.
Define graph G2 on the same set of vertices with adjacency matrix N, where
$$N_{ij} =\left\{ {\begin{array}{*{20}{c}} {1 \ \ \text{if} \ \ {M_{ij}} > 0 \ \ \text{or} \ \ P_{ij} > 0, \ \text{where} \ \ P = {M^2}}\\ {0, \ \ \ \ \ \text{otherwise}} \end{array}} \right.$$
Which one of the following statements is true?
Consider the following matrix.
$$\left( {\begin{array}{*{20}{c}} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{array}} \right)$$
The largest eigenvalue of the above matrix is ______