Here is a longer list of problems and solutions:
A random process is a collection of random variables indexed by a parameter, usually time. In electrical engineering, random processes are used to model and analyze signals and systems that vary randomly over time.
The probability of decoding a codeword incorrectly is given by: Here is a longer list of problems and
A control system has a transfer function H(s) = 1 / (s + 1). If the input to the system is a random signal X(t) with a mean of 0 and a variance of 1, what is the mean and variance of the output signal Y(t)?
Probability and random processes are fundamental concepts in electrical engineering, playing a crucial role in the analysis and design of communication systems, signal processing, and control systems. This paper provides an overview of the key concepts in probability and random processes, with a focus on their applications in electrical engineering. If the input to the system is a
A random signal X(t) has a power spectral density S_X(f) = 1 / (1 + f^2). What is the autocorrelation function R_X(τ)?
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R_X(τ) = F^(-1) [S_X(f)] = e^(-|τ|)