Probability Distributions: Exponential Distribution

Question 1

Exponential Distribution

Answer 1

• Continuous distribution, widely used.
• Estimates the lapse of time between the independent events.
  
  • In other words, it describes the times in between events a process in which events occur continuously and independently at a constant average rate.
• Exponential distribution is the time between events in a Poisson process
  
  • If the number of occurrences follows a Poisson distribution, the lapse of time between these events is distributed exponentially
• Used to model items with a constant failure rate

Question 2

Key Difference between Poisson and Exponential

Answer 2

Question 3

The formula of Exponential Distribution

Answer 3

• The probability density function (pdf)
• The cumulative distribution function (cdf)
• The mean and standard deviations are equal

Question 4

Shape of the Exponential Distribution

Answer 4

The distributions of a random variable shows the exponential distribution is shown below. The curve declines continuously, implying that as x rises, the probability attached to it decreases.

Question 5

When is exponential distribution used?

Answer 5

• Describes the times in between events a process in which events occur continuously and independently at a constant average rate.
• To describe the time between successive occurrences when all occurrences follow an exponential
• To predict the length of time that properly maintained equipment will operate
• Approximate the time between outcomes
• When a probability of an outcome is consistent throughout the time period

Applications

• The number of hours a mobile phone runs before its battery dies out.
• The time it takes for a call center executive respond to a caller
• The probability of receiving a phone call in the next 30 minutes
• The amount of time (may be in months) a car battery lasts

Question 6

Exponential Distribution Example

Answer 6