Theorem: A full m-ary tree with: (i) n vertices has i = (n - 1)/m internal vertices and I = [(m - 1)n + 1]/m leaves, (ii) i internal vertices has n = mi + 1 vertices and l = (m - 1)i + 1 leaves, (iii) I leaves has n = (ml - 1) /(m -1) vertices and i = (1 -1)/(m - 1) internal vertices. * In each Distribution Problem, determine the type of the distribution and write the X's distribution. X p(x) Values of X E(X) V(x) b-a+1 asxsb b+a (b-a+2)(b-a) 2 12 QP' (1-PM-X X= 0.1_n np np(1-P) x! x = 0.1,2. ... (1-p)*-1p x =1,2,3... 1-P p 2 K_1 (1-P)*-Kp* x=k,k+1.. k(1-P) p2 MN-M X n-x max (0,M + n-N) M nM(N- M)(N -n) N Sxs min (M.n) N N2 (N-1)4. (2 points each True or False? Explain your answer or give a counter example. i). If every vertex in a tree has odd degree, the number of edges in the tree may be either odd or even. ii) Let G be a connected graph. If G has no cut edge, then G has no out vertices. 5. (4 points A chain letter starts when a person sends a letter to 5 people. Each person who sends the letter to 5 other people who have never received it or does not send it to anyone. Suppose that 10,000 people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter? How many people do not send it out? 6. (4 points Dene the graph Km,\" How many edges does that graph has