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) ((t-,)* 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) (1+eat) ( b ) - ( 1 +e 2at ) ( 0 ) ; ( 1 - ext ) (d) (1-e-2at ) (e) None. (2) P(X (t) =-1) = (a) (1-e-2at) (b ) " (1-en) (c) - (1te 2x ) (d) (1+e-at) (e) None. (3) E{X(t) } = (a) -e-2at (b) e-21t (c) 2e-21t (d) 0 (e) None (4) R(t, , t, ) = (a) -e-27 -12 (b) e-24-121 (c) e-al-12 (d) elk-12 (e) None