4. Let n be a Poisson point process with parameter 1, that is P(n, the number of random points arrive in(t,t, ), = k) = e-(12-1) (a(12-1,)k k ! (1, if k is odd in (0,t). Define a new stochastic process as X(t)= -1, if k is even in (0,t). (1) P(X(t) = 1) = (a) -(1text ) ( b ) - ( 1 +e- 2at ) (0 ) ; ( 1 - eht ) (d) (1-e-2at) (e) None. (2) P(X (t) =-1)= (a) -(1-e-2at ) (b ) ? (1-e-4 ) ( c ) 7 ( 1 +e- 2 21 ) (d) (1+e-at) (e) None. (3) E{X(1)) = (a) -e-2at (b) e-24t (c) 2e-24t (d) 0 (e) None (4) R(t, , t, ) = (a) -e-221,-121 (b) e-2214-121 (c) e-21-121 (d) elk,-12 (e) None