3. Fifteen percent of the cars parked in lot A are equipped with car alarms. The

Question

3. Fifteen percent of the cars parked in lot A are equipped with car alarms. These cars are randomly distributed throughout the lot. Jimmy is a car burglar who can successfully jimmy the locks on 75% of the cars he encounters, independent of whether the car is equipped with an alarm. Jimmy attempts to break into successive cars in the lot until he encounters one with an alarm, at which point the car alarm goes off and he flees the lot. Let N be the number of cars he attempts to break into, up to and including the first alarm-equipped car. (a) Give the distribution of N, including any necessary parameters and definition of success. (b) What is EIN]? (c) It turns out that on a particular night, Jimmy attempts to break into N = 9 cars before having to flee. Let Y be the number of cars (out of the 8 preceding) that Jimmy successfully breaks into Give the distribution of Y, including any necessary parameters and definition of success, and find the probability that Y is 6 or more.

Explanation / Answer

(a) Here the distribution of N is geometric distribution with success probability p = 0.15. Here definition of success is the first alarmed car jimmy break into or upto.

f(N) = (1-p)N-1 p =  0.15 * 0.85N-1

(b) Here E[N] = 1/p = 1/0.15 = 6.67

(c) Here the distribution of Y is binomial distribution where parameters n = 8 and p = 0.75

f(Y) = 8CY (0.75)y(0.25)8-y

Pr(Y >= 6) = 1- BIN(Y < 6 ; 8 ; 0.75) = 1 - 0.3215 = 0.6785

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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