Exponential Distribution Question

In summary, the conversation discusses the concept of memorylessness and its relation to probability distributions. It is mentioned that there are only two distributions that exhibit memorylessness. Additionally, the expected remaining life of a tiger is asked, with the answer being 5 years. The discussion also touches on the implications of a constant probability distribution for forward looking expectations.
  • #1
Caution
9
0
Hi all,
Can anyone teach me this problem ? Thanks

The life of a tiger is exponentially distributed with a mean of 15 years.If a tiger is 10 years old, what is the expected remaining life of the tiger?

A 5 years
B 10 years
C 15 years
D Longer than 15 years
 
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  • #2
Can you tell me your understanding of 'memorylessness'? What distributions have this property and what does it mean?
 
  • #3
StoneTemplePython said:
Can you tell me your understanding of 'memorylessness'? What distributions have this property and what does it mean?

It means the probability distribution of the remaining time until the event occurs always is the same, regardless of how much time (s) already has passed. So I'm guessing the answer is 5?
 
  • #4
Caution said:
It means the probability distribution of the remaining time until the event occurs always is the same, regardless of how much time (s) already has passed. So I'm guessing the answer is 5?

so if the probability distribution is the same whether 0 years have passed or 7 years have passed, then what does that tell you about forward looking expectations?

Also do you know which distributions exhibit memorylessness? (There are only 2...)
 

Related to Exponential Distribution Question

1. What is the exponential distribution?

The exponential distribution is a probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant rate. In simpler terms, it is a probability model that is used to describe the time it takes for a certain event to occur.

2. How is the exponential distribution different from other distributions?

The exponential distribution is unique in that it is memoryless, meaning that the probability of an event occurring in a given time interval is not affected by how much time has passed. This is in contrast to other distributions, such as the normal distribution, where the probability of an event occurring depends on how much time has already passed.

3. What are some real-life examples of the exponential distribution?

The exponential distribution can be used to model the time between phone calls, earthquakes, radioactive decay, and the lifespan of certain products. It is also commonly used in queuing theory and reliability engineering.

4. How is the exponential distribution related to the Poisson distribution?

The exponential distribution is closely related to the Poisson distribution, as it is often used to model the time between events in a Poisson process. In fact, if the number of events in a Poisson process is recorded in a fixed time interval, the distribution of those counts will follow a Poisson distribution.

5. How is the exponential distribution used in statistics?

The exponential distribution is commonly used in statistics to model the time-to-failure of products or systems. It is also used in survival analysis to estimate the probability of an event occurring within a certain time period. Additionally, it is used in hypothesis testing to determine if two samples come from populations with the same mean or to compare the mean of a sample to a known value.

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