Write a simple simulation program that generates randomly

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Reference no: EM132392435

CEN 601

Project

Consider a discrete time discrete state random processes X(i, ζ), with the equiprobable two values random variable ζ defined by:

• if ζ = N, the realization of the process X(i, N) will be formed by selecting a discrete random number Uniformly from the values [1, 2, ..., N], and repeating the experiment for i = 1, 2, · · ·;

• if ζ = M, the realization of the process X(i, M) will be formed by selecting a discrete random number Uniformly from the values [1, 2, ..., M], and repeating the experiment for i = 1, 2, · · ·.

Assume that N < M, and denote the realizations X(i, N) by Type I, and X(i, M) by Type II.

Consider an outside observer who follows a realization of one of the two processes, and should determine the type of the process after repeating the experiment K times.

1. What can you conclude about the type of the process in each of these cases:

(a) if any one of the observations is greater than N;

(b) if the observations are less or equal to N.

2. Now consider the second case. After K consecutive observations {oi ≤ N; i = 1, 2, · · · , K}, it is needed to establish a model to classify this unknown process.

(a) What is the probability density of o_i , assuming that the unknown process is of:

i. Type I,.

ii. Type II.

(b) Given K, find the probability that the unknown process is of:

i. Type I.

ii. Type II

3. Write a simple simulation program that generates randomly X(i, N) and X(i, M) to check your results in (1) and (2). Try various values of N and M with different differencesM - N, and check the effect of the number of generated numbers.

Reference no: EM132392435

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