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 tuo or three sentences, in English, explaining why the chosen model in part (b) is the appropriate one

Explanation / Answer

a) X represent the number of attempts required until 2 or 4 appear first time

b) X follow geometric distribution

parameter p = 2/10 = 0.2

c)

P(X = k) = (1-p)^(k-1) * p

P(X = 3) = 0.8^2 * 0.2 = 0.128

d)

The geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p. If the probability of success on each trial is p

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.