Please simulate a random variable {Y:i=0,1,2,...T} that starts at Yn=0. In particular, at every time step i +1 when you

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Please Simulate A Random Variable Y I 0 1 2 T That Starts At Yn 0 In Particular At Every Time Step I 1 When You 1 (45.93 KiB) Viewed 27 times

Please simulate a random variable {Y:i=0,1,2,...T} that starts at Yn=0. In particular, at every time step i +1 when you obtain Y, it is based on the following information: P(Y1 = +1 Y = j) =P (Eq. 1) P(Y. = 3-1 Y = j)=1-p (Eq. 2) where j is an integer that jeZ = {...-2,-1.0.1, 2.... Note that you will need to first generate the random numbers based on the following LCG generator (Note: Xo = 1268): Xi+1 = (57015 + 755391831 * X)mod 215, i = 0,1,2 ....T Random number: Ri+1 If the random number obtained at each time step i is less than p, then you will use Eq. 1 to specify You otherwise, you will use Eq. 2. (a) Generate 6 realizations {91,Y2...., yo} of the process for p = 0.51; (3 points) (b) Generate 6 realizations {y1, Y2,...,Y6} of the process for p = 0.68; (3 points) (c) Plot the first 50 samples {yı,Y2,..., Yso) you obtained for p = 0.51 and p = 0.68, respectively, on one graph. Make sure your graph is clear enough to present the Y vs.time step. (4 points) = 215