A Chebyshev interval with a poisson distribution

In summary, a geophysicist can determine the age of a zircon by counting the number of uranium fission tracks on a polished surface, which follows a Poisson distribution. For a zircon with an average of seven tracks per square centimeter, an interval that includes at least 60% of the sample values of fission track counts can be obtained using Chebyshev's theorem. The standard deviation is not needed as the Poisson distribution only has one parameter, lambda, which is equal to the mean and variance. Solving for k will give the desired interval.
  • #1
Snarf
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[SOLVED] A Chebyshev interval with a poisson distribution

Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface; the number of these uranium fission tracks on this surface follows a Possion distribution. A particular zircon is of such an age that the average number of tracks per square centimeter is seven. Give an interval that will include at least 60% of the sample values of fission track counts obtained from a large number of square centimeter samples.

I know this problem require chebyshevs theorem, but I don't have the standard deviation. How do I figure this out?
 
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  • #3
I think I've figured it out. Lambda is the mean and the variance for a Poisson distribution. So SQR 100 is the standard deviation in this problem. From there its a matter of solving for k and finding the interval.
 

FAQ: A Chebyshev interval with a poisson distribution

What is a Chebyshev interval?

A Chebyshev interval is a statistical concept that represents a range of values within which a certain percentage of data points lie. It is calculated using the mean and standard deviation of a dataset, and is often used to estimate the spread of a distribution.

How is a Chebyshev interval different from a confidence interval?

A Chebyshev interval is a more generalized measure of spread, as it can be calculated for any type of distribution. On the other hand, a confidence interval is specific to the normal distribution and requires certain assumptions to be met. Additionally, a Chebyshev interval only provides a lower bound for the percentage of data points within the interval, while a confidence interval gives a specific range with a certain level of confidence.

What is a Poisson distribution?

A Poisson distribution is a discrete probability distribution that is often used to model the number of occurrences of a certain event within a fixed time or space interval. It is characterized by a single parameter, lambda, which represents the average number of occurrences in the given interval.

How is a Poisson distribution related to a Chebyshev interval?

A Chebyshev interval can be used to estimate the spread of a Poisson distribution by setting the mean equal to lambda and using the standard deviation as a measure of spread. However, the Chebyshev interval may not provide an accurate estimate for the percentage of data points within the interval, as the Poisson distribution does not follow the same shape as a normal distribution.

Can a Chebyshev interval be used for any type of dataset?

Yes, a Chebyshev interval can be calculated for any type of dataset, as long as the mean and standard deviation are known. However, it may not provide the most accurate estimate of the spread for distributions that do not follow a normal shape.

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