In Santa Theresa, false alarms are received at the downtown...

Name: Problem 45, Chapter 7: Applied Statistics in Business and Economics
Uploaded: 2021-12-13T11:56:11-08:00
Duration: 1 min 14 s
Channel: Hast Aggarwal
Description: In Santa Theresa, false alarms are received at the downtown fire station at a mean rate of 0.3 per day. (a) What is the probability that more than 7 days will pass before the next false alarm arrives? (b) Less than 2 days? (c) Explain fully.

In Santa Theresa, false alarms are received at the downtown fire station at a mean rate of 0.3 per day. (a) What is the probability that more than 7 days will pass before the next false alarm arrives? (b) Less than 2 days? (c) Explain fully.

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Key Concepts

Poisson Process

A Poisson process is a statistical model that represents events occurring randomly in time or space at a constant average rate. It is often used to model arrivals or occurrences of events such as false alarms. The key feature of a Poisson process is that the events occur independently of one another and the number of events in disjoint intervals are independent.

Exponential Distribution

The exponential distribution describes the time between consecutive events in a Poisson process. It characterizes the waiting time until the next event occurs, using a rate parameter often denoted by ?. The probability of waiting more than a certain amount of time is given by the survival function, which is an exponential decay function.

Memoryless Property

The memoryless property is a unique characteristic of the exponential distribution. It means that the probability of an event occurring in the next time interval is independent of how much time has already elapsed. This property simplifies the calculation of probabilities for waiting times, regardless of the past history.

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