The number of knots in a particular type of wood has a...

Name: Problem 131, Chapter 3: Mathematical Statistics with Applications
Uploaded: 2021-05-07T12:59:27-08:00
Duration: 1 min
Channel: Christopher Stanley
Description: The number of knots in a particular type of wood has a Poisson distribution with an average of 1.5 knots in 10 cubic feet of the wood. Find the probability that a 10 -cubic-foot block of the wood has at most 1 knot.

The number of knots in a particular type of wood has a Poisson distribution with an average of 1.5 knots in 10 cubic feet of the wood. Find the probability that a 10 -cubic-foot block of the wood has at most 1 knot.

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Key Concepts

Cumulative Probability

Cumulative probability is the sum of probabilities for a random variable taking on values less than or equal to a specified number. In the context of the Poisson distribution, it is obtained by summing the PMF values for all counts up to that number, which helps in determining the likelihood of observing at most a certain number of events.

Probability Mass Function (PMF)

The probability mass function for a Poisson distributed variable gives the probability of observing exactly k events. It is expressed by the formula P(X=k) = (e^(-?) * ?^k) / k!, where k is a non-negative integer, enabling the calculation of individual event probabilities.

Poisson Distribution

The Poisson distribution is a discrete probability distribution used to model the number of times an event occurs in a fixed interval of time or space. It is based on the assumption that these events occur with a known constant mean rate and independently of the time since the last event.

Rate Parameter (?)

The rate parameter, denoted as ?, represents the expected number of events occurring in a specified interval. This parameter is central to the Poisson distribution, determining its shape and the probabilities of different numbers of events.

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