16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde x(t) T +2T to is uniformly distributed over(0,T) Change points are periodic with period T Amplitudes independent with a, a Ru(r)=E[r(Ox(t+r) P(I or more change points in)a+ P(No change point in pa TST +a,≤r R R XX f 816.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 8 of 8 0t is uniformly distributed over (0, ) T Change points are periodic with period T Amplitudes independent with 2 a a, [ ] 2 2 2 2 2 2 2 ( ) () ( ) (1 or more change points in ) (No change point in ) 1 , 1 , ( ) , xx a xx R E xtxt P aP a a aT T T a T R T a T τ τ τ τ τ τ τ τ σ τ τ τ = + = + ⎛ ⎞ = +− ≤ ⎜ ⎟ ⎝ ⎠ ⎧ ⎛ ⎞ ⎪ ⎜ ⎟ −+ ≤ = ⎨ ⎝ ⎠ ⎪ > ⎩