Solving Poisson Distribution Homework for 50 Liters of Sediment

In summary, the conversation discusses the calculation of the probability of finding 1 or more prehistoric artifacts in a 50-liter sample of sediment with an artifact density of 1.0 per 10 liters. The equation used is P(r) = (e^-lambda)*(lambda^r)/r!, but it is unclear what the value of lambda should be. The random variable r represents the number of artifacts found in the sample, and the problem asks for the probability of finding one or more artifacts.
  • #1
magma_saber
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Homework Statement


In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.0. Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your 50 liters of sediment. Find the probability that you will find 1 or more artifacts in the 50 liters of sediment. Round your answer to the nearest ten thousandth.


Homework Equations


P(r) = (e^-lambda)*(lambda^r)/r!

The Attempt at a Solution


What is lambda? is it 10? or is it 10/50=0.2? i can't seem to figure it out.
i think r = 1
 
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  • #2
λ is the number of artifacts in the 50 liters of sediment on average.

P(1) would be the probability you'd find exactly one artifact in the 50-liter sample, but the problem is asking you to find the probability of finding one or more. So you can't just set r=1 to get the answer you're looking for.
 

1. What is Poisson distribution and how is it used in solving sediment homework?

Poisson distribution is a mathematical probability distribution that is used to model the number of events that occur in a specific time interval or space. It is used in solving sediment homework by calculating the probability of a certain number of sediment particles occurring in a specific volume of sediment.

2. What are the steps for solving Poisson distribution homework for 50 liters of sediment?

The steps for solving Poisson distribution homework for 50 liters of sediment are as follows:

  1. Determine the average number of sediment particles per liter of sediment.
  2. Calculate the mean (λ) using the formula λ = np, where n is the number of liters (50) and p is the probability of a sediment particle occurring in one liter.
  3. Use the Poisson distribution formula P(x; λ) = (e^-λ)(λ^x)/x!, where x is the number of sediment particles we want to find the probability for.
  4. Substitute the value of λ and x into the formula and solve for P(x; λ).

3. How does the Poisson distribution differ from other probability distributions?

The Poisson distribution differs from other probability distributions in that it is used to model the number of discrete events occurring in a specific interval or space, while other distributions such as the normal distribution are used for continuous variables. Additionally, the Poisson distribution uses only one parameter (mean) to describe the data, while other distributions may use more than one parameter.

4. Can Poisson distribution be used for any type of sediment?

Yes, Poisson distribution can be used for any type of sediment as long as the number of events (sediment particles) occurring in a specific volume or space can be modeled as a discrete random variable. This means that the sediment particles must be independent of each other and the probability of a particle occurring in a specific volume must be the same for all particles.

5. Are there any limitations to using Poisson distribution for solving sediment homework?

Yes, there are some limitations to using Poisson distribution for solving sediment homework. One limitation is that it assumes that the rate of sediment particle occurrence is constant over time and space, which may not be true in all cases. Additionally, if the average number of sediment particles per unit volume is very small, the Poisson distribution may not be an accurate model.

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