An Inventory Model - A hot dog vendor operates a stand where the number of hot dogs he sells each day is modeled as a Poisson random variable with a mean value of 100. Let X [k] represents the number of hot dogs the vendor has at the beginning of each day. At the end of the day, if his inventory of hot dogs on hand falls below some minimum value, a, then the vendor goes out that evening and purchases enough hot dogs to bring the total of his inventory to ß. Write an equation to describe the elements of the transition probability matrix, p i, j, for this inventory process.
Answer to relevant QuestionsA Web Search Engine Model - Suppose after we enter some keywords into our web search engine it finds five pages that contain those keywords. We will call these pages A, B, C, D, and E. The engine would like to rank the pages ...Let be a deterministic periodic waveform with period to. A random process is constructed according to X (t) = s (t – T) Where T is a random variable uniformly distributed over [0, to]. Show that the random process X (t) ...Develop a formula to compute the RMS bandwidth of a random process, X (t), directly from its autocorrelation function, RXX (τ). Show that the estimator for the autocorrelation function, ṘXX (τ), described in Equation (10.26) is unbiased. That is, show that E [ṘXX (τ)] = RXX (τ). Consider a random process of the form , X (t) = b cos (2πΨt + θ) Where is a constant θ, is a uniform random variable over [0, 2π], and Ψ is a random variable which is independent of and has a PDF, fΨ (Ψ). Find the ...
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