A student needs to know details of a class assignment that is due the next day a

Question

A student needs to know details of a class assignment that is due the next day and decides to call fellow class members for this information. She believes that for any particular call the probability of obtaining the necessary information is 0.40. She decides to continue calling class members until the information is obtained. Let the random variable X denote the number of calls needed to obtain the information. a) Find the probability function of X. b) Find the cumulative probability function of X. c) Find the probability that at least three calls are required.

Explanation / Answer

For a given phone call the probability of being unsuccessful is: 1 - 0.4 = 0.6. (a) P(X=1) = 0.4 P(X=2) = P(unsuccessful on call 1 and successful on call 2) = (0.6)(0.4) = 0.24 P(X=3) = P(unsuccessful on calls 1 and 2 and successful on call 3) = (0.6)(0.6)(0.4) In general, P(X=x) = (0.6)x-1(0.4) for x = 1, 2, 3, 4, . . . (b) F(x) = 1 - (0.6)x for x = 1, 2, 3, 4, . . . (c) P(X = 3) = 1 - P(X < 3) = 1 - [P(X=1) + P(X=2)] = 1 - (0.4 + 0.24) = 0.36

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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