PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A= A² A²)

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.