Stochastic process.

1. Let V = {1, 2, 3, . . . , n} a set of verteces. We can construct random

graphs by assinging, to each vertex i another vertex X(i). In this way the

random graph has edges

E = {(1, X(1)),(2, X(2)),(3, X(3)), . . . ,(n, X(n))}

X is a random variable such that P(X(i) = k) = 1/n for all i, k = 1, . . . , n

that is any vertex is assigned to any other vertex (including itself) with

equal probability. Compute the probability the graph is connected in the

following 2 cases: n = 3 and n = 4