The process x(t) is WSS and normal with E{x(t)} = 0 and R(T)=4e-²²1, (a) Find P(x(1) ≤ 3}. (b) Find E{[x(t + 1) − x(t − 1)}²}.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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**Exercise 9.8**

The process \( x(t) \) is Wide-Sense Stationary (WSS) and normal, with the following characteristics:

- Mean: \( E\{x(t)\} = 0 \)
- Autocorrelation function: \( R(\tau) = 4e^{-2|\tau|} \)

**Tasks:**

(a) Calculate the probability \( P\{x(t) \leq 3\} \).

(b) Find the expected value \( E\{[x(t + 1) - x(t - 1)]^2\} \).
Transcribed Image Text:**Exercise 9.8** The process \( x(t) \) is Wide-Sense Stationary (WSS) and normal, with the following characteristics: - Mean: \( E\{x(t)\} = 0 \) - Autocorrelation function: \( R(\tau) = 4e^{-2|\tau|} \) **Tasks:** (a) Calculate the probability \( P\{x(t) \leq 3\} \). (b) Find the expected value \( E\{[x(t + 1) - x(t - 1)]^2\} \).
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