Problem 3. A computer has been programmed to generate a series of random digits.

Question

Problem 3. A computer has been programmed to generate a series of random digits. The process stops when either a 2 or a 4 appear (a) Define a random variable X appropriate for this problem. In other words, with a sentence in English state what X measures. b) What classical model is appropriate for the random variable X? What are the values of the corresponding parameters? (c) What is the probability that the process stops after the third digit is generated? (d) Write two or three sentences, in English, explaining why the chosen model in part (b) is the appropriate one.

Explanation / Answer

a. Let X=no. of steps required for the process to get stopped.

b. X~Geometric(p) where p=Probability of occurrence of 2 or 4=2/10 = 0.2

c. Probability that the process stops after the 3rd digit is generated= (1-0.2)2 * 0.2=0.128

d.

Geometric distribution deals with number of trials required to get first success or the number of failures before the first success. Here, the stoppage of the process of the computer may be treated as a success. So, we can model this problem with geometric distribution as we can obtain the probabilities for the process to stop in different stops.

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