Math Problem Solver

Consider the sequential detection framework:

Under H0: y1, y2, · · · are i.i.d with marginal pdf f0 = N(1, 2)

Under H1: y1, y2, · · · are i.i.d with marginal pdf f1 = N(−1, 1)

Here N denotes Gaussian pdf. We have the constraints PF = 0.001 and PM = 0.01.

(a) Find average number of observations used by SPRT under each hypothesis.

(b) Given the set of observations {y1, y2, · · · } = {0.3,−2.1, 1.7, 4.5, 3.5,−3, · · · },

implement the SPRT rule and check if SPRT stops before time index n = 7.

If yes, when will it stop and what will be the hypothesis chosen? (c) (c) For the same f0 and f1 given in the above problem, consider the change detection

problem with false alarm rate constraint α = 0.05.

(d) For the observation set given above , implement the CUSUM algorithm and check if the alarm time happens before time index n = 7. If yes, what is the alarm time?