A random signal X(t) has a Gaussian distribution with mean 0 and variance 1. What is the probability that X(t) > 2?
Yes, X(t) is stationary because its autocorrelation function depends only on the time difference τ, not on the absolute time t.
Here is a longer list of problems and solutions: A random signal X(t) has a Gaussian distribution
The mean of the output signal Y(t) is given by:
The variance of the output signal Y(t) is given by: A random signal X(t) has a Gaussian distribution
P(error) = 0.6 * 0.1 + 0.4 * 0.1 = 0.1
P(X(t) > 2) = Q(2) = 1 - Φ(2) ≈ 0.023 A random signal X(t) has a Gaussian distribution
I hope this helps! Let me know if you have any questions or if you'd like me to elaborate on any of these topics.