# Question: Suppose that the time between successive occurrences of an event

Suppose that the time between successive occurrences of an event follows an exponential distribution with a mean of 1/λ minutes. Assume that an event occurs.

a. Show that the probability that more than 3 minutes elapses before the occurrence of the next event is e –3λ.

b. Show that the probability that more than 6 minutes elapses before the occurrence of the next event is e -6λ.

c. Using the results of parts (a) and (b), show that if 3 minutes have already elapsed, the probability that a further 3 minutes will elapse before the next occurrence is e -3λ. Explain your answer in words.

a. Show that the probability that more than 3 minutes elapses before the occurrence of the next event is e –3λ.

b. Show that the probability that more than 6 minutes elapses before the occurrence of the next event is e -6λ.

c. Using the results of parts (a) and (b), show that if 3 minutes have already elapsed, the probability that a further 3 minutes will elapse before the next occurrence is e -3λ. Explain your answer in words.

**View Solution:**## Answer to relevant Questions

Swapna David is a customer assistant consultant for Acme Information Systems, who provides assistance for computer users. The mean number of calls per hour is 40 from across the United States and calls are independent. She ...A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation ...The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb ...A consultant knows that it will cost him $10,000 to fulfill a particular contract. The contract is to be put out for bids, and he believes that the lowest bid, excluding his own, can be represented by a distribution that is ...A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes. a. What is the probability that a single ...Post your question