Please use R program Poisson distribution part 2 A random variable X is known to be drawn from a Poisson distribution. A

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Please use R program
Poisson distribution part 2
A random variable X is known to be drawn from a Poisson
distribution. An observation is made: n = 6 is obtained.
• State the precise definition of p-value and perform a
one-sided test for the null that λ = 3.3.
• Calculate the likelihood ratio for H1 : λ = 4.1 and H2 : λ =
2.2.
• Plot a log-likelihood function in the range 2 ≤ λ ≤ 14.
• Calculate a credible interval for λ, using a
2-units-of-support criterion. An approximate answer is fine
• Excellence question: calculate a confidence interval as per
the end of chapter 3 in the course manual; compare the confidence
interval with the credible interval above. One decimal place
sufficient.