Consider a two- state Markov chain with a general transition probability matrix
Where 0 < p, q< 1. Find an expression for the - step transition probability matrix, P n.
Answer to relevant QuestionsFor the general two- state Markov chain of Exercise 9.8, suppose the states are called 0 and 1. Furthermore, suppose Pr (X0= 0)= s and Pr (X0= 1) = 1 – s . (a) Find Pr (X1= 0, X2= 1). (b) Find Pr (X1= 1 | X0= 0, X2= 0). ...Two zero- mean discrete random processes, X [n] and Y [n], are statistically independent and have autocorrelation functions given by RXX [k] = (1/ 2) k and RYY [k] = (1/ 3) k . Let a new random process be Z [n] = X [n] + Y ...Find the PSD of the process Let Wn be an IID sequence of zero- mean Gaussian random variables with variance. Define a discrete- time random process, X[ n] = pX[ n – 1]+ Wn, n = 1, 2, 3, … where X[ 0] = W0 and is a ...Using the expression for Var (ṘXX (τ))found in Exercise 10.26, show that as | τ | → 2t o, Var (ṘXX (τ)) > Var (X(t)), and therefore, the estimate of the autocorrelation function is at least as noisy as the process ...Let Where all of the ωn are non- zero constants, the an are constants, and the θn are IID random variables, each uniformly distributed over [0, 2π]. (a) Determine the autocorrelation function of X (t). (b) Determine the ...
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