Let Yn be an i.i.d. sequence with P {Yn process Xn as == -1} = 2P...

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Let Yn be an i.i.d. sequence with P {Yn process Xn as == -1} = 2P {Y = 2} = 2/3. Define the random Xo = Yo, Xn = a Xn-1 + Yn, ne z+, where a [0, 1] is a constant. X is an auto-regressive (AR) process of order 1. (a) Assume a = 1. Estimate the probability P {X1000 > 1}. Explain and justify your answer. (Your answer may involve the Q function.) Answer the rest of the question for a = 1/2. (b) Find E [Xn]. (c) Find Var (Xn). (d) Find E[Xn Xn+k] for k > 0. (e) Is Xn wide sense stationary? Why? Let Yn be an i.i.d. sequence with P {Yn process Xn as == -1} = 2P {Y = 2} = 2/3. Define the random Xo = Yo, Xn = a Xn-1 + Yn, ne z+, where a [0, 1] is a constant. X is an auto-regressive (AR) process of order 1. (a) Assume a = 1. Estimate the probability P {X1000 > 1}. Explain and justify your answer. (Your answer may involve the Q function.) Answer the rest of the question for a = 1/2. (b) Find E [Xn]. (c) Find Var (Xn). (d) Find E[Xn Xn+k] for k > 0. (e) Is Xn wide sense stationary? Why?