A hen lays N eggs, where N has the Poisson distribution with parameter λ. Each egg...

A hen lays N eggs, where N has the Poisson distribution with parameter λ. Each egg hatches with probability p independently of the other eggs. Let K be the number of chicks. What is the covariance between N and K?

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orchestra answered 2 years ago

For the Poisson Distribution a. Is λ×T a parameter of position, scale, shape or a combination?...

For the Poisson Distribution a. Is λ×T a parameter of position, scale, shape or a combination? Explain. b. We can treat “λ×T” as a single parameter, but they actually represent two parameters: λ and T. Say you stand by the side of the road and count the number of cars that pass by you in one minute. After repeating this process 10 times you find the average number of cars that pass in 10 minutes. In this case, what is...

A poultry farmer wants to know which breed of hen lays more eggs. A random sample...

A poultry farmer wants to know which breed of hen lays more eggs. A random sample of 60 values of the average daily egg production by the Rhode Island Red hens had a sample mean of 0.765 egg per hen and a sample standard deviation of 0.11. A random sample of 50 values of the average daily egg production by the Plymouth Rock hens had a mean of 0.559 egg per hen and a standard deviation of 0.09. Determine the...

The distribution of the number of eggs laid by a certain species of hen during their...

The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 36 eggs with a standard deviation of 18.3. Suppose a group of researchers randomly samples 47 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 1,000 times, and build a distribution of sample means. A) What is this distribution called? B) Would you expect the...

The number of imperfections in an object has a Poisson distribution with a mean λ =...

The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad...

A freerange egg farmer has a field of 4,000 m2 area. On this field there are currently 500 chicken. Each chicken lays 150 eggs per year.

A freerange egg farmer has a field of 4,000 m2 area. On this field there are currently 500 chicken. Each chicken lays 150 eggs per year. As space and food is limited on the field, for every tenth chicken added to the field, each chicken lays 1 egg less per year. How many eggs per year can the farmer expect at most?

Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is...

Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is binomial(2,1/3). (a) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 1. (b) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 2 Hints: Because of its prior distribution, λ can take only three values, 0,1,2. Don’t expect its posterior distribution to be any...

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆.

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆. To estimate 𝜆 we obtain the random sample 𝑋1,𝑋2, … , 𝑋n.a. Find the Fisher information is a single observation using two methods.b. Find the Cramer-Rao lower bound for the variance of an unbiased estimator of 𝜆.c. Find the MLE of 𝜆 and show that the MLE is an efficient estimator.

Suppose X1, X2, . . ., Xn are iid Poisson random variables with parameter λ. (a)...

Suppose X1, X2, . . ., Xn are iid Poisson random variables with parameter λ. (a) Find the MVUE for λ. (b) Find the MVUE for λ 2

Let XiXi for i=1,2,3,…i=1,2,3,… be a random variable whose probability distribution is Poisson with parameter λ=9λ=9....

Let XiXi for i=1,2,3,…i=1,2,3,… be a random variable whose probability distribution is Poisson with parameter λ=9λ=9. Assume the Xi are independent. Note that Poisson distributions are discrete. Let Sn=X1+⋯+Xn. To use a Normal distribution to approximate P(550≤S64≤600), we use the area from a lower bound of __ to an upper bound of __ under a Normal curve with center (average) at __ and spread (standard deviation) of __ . The estimated probability is __

Let Y denote a random variable that has a Poisson distribution with mean λ = 6....

Let Y denote a random variable that has a Poisson distribution with mean λ = 6. (Round your answers to three decimal places.) (a) Find P(Y = 9). (b) Find P(Y ≥ 9). (c) Find P(Y < 9). (d) Find P(Y ≥ 9|Y ≥ 6).

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