Consider a variable X known to have a Poisson distribution. We will consider a null hypothesis...

Consider a variable X known to have a Poisson distribution. We will consider a null hypothesis that λ = 3.1 (this question will consider one-sided tests only). Suppose we observe X = 7.

(a) State the precise definition of p-value for our observation of 7 events

(b) Calculate the p-value for this observation and interpret

(d) Again for the observation of 7 events, plot a log-likelihood function for λ, and estimate a credible interval for λ. A rough estimate is fine. (

e) (harder) A Bayesian comes along and announces that his prior for λ is an exponential distribution with rate 0.6 (that is, P(λ) ∝ e −0.6λ ). Plot his posterior likelihood function for λ, given the observation of 7. hint: you can calculate the density of the exponential distribution using dexp(x,rate=0.6).

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orchestra answered 1 year ago

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