let (N., +>=0) be a poisson counting process with rate A = 2, and define t,=10, t2=18, n,=4, n2=10. a) Determine P( M = n1, Nez = n2) b) Determine P( N (1, ti] = n1, N(t1 - 1, to] = n2) c)Determine PON (1, ti] = n1\\N(t1 - 1, to] = n2) d) determine PON (1, ti] ) e) Determine PON (1, ti]\\N (1 - 1, to] = n2) f) Dertermine PON (1 - 1, to] [N (1, ti] = n1) 9) show that, for 0 0(Ns|N = n) ~ Bin(n, s/t) h) Denote by /k the time of the k-th event. Show that, given Ny=1, T, is uniformly distributed on [0,1] i) Determine the pdf of T, given N