Suppose the number of people in a gym each morning has a Poisson distribution, but with the rate parameter/mean A unknown. The probability mass function for the Poisson distribution is given by A exp(-A) p(x|A) = x! (5) and the observed data is {5, 7, 4}. (a) Create R vectors to represent a set of possible A values ranging from 0.01 to 100 in steps of 0.001, and create an R vector to represent a log-uniform prior distribution, where the probabilities are proportional to 1/A. Normalise the vector of prior probabilities so that it adds to 1. Hint: This question is the same as 3(d). (b) Create an R vector representing the likelihood values. You can use dpois () or the given formula. (c) Compute and plot the posterior distribution. (d) Calculate the posterior probability that A is greater than 5.

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Suppose the number of people in a gym each morning has a Poisson distribution, but with the
rate parameter/mean A unknown. The probability mass function for the Poisson distribution is
given by
A exp(-A)
p(x|A) =
x!
(5)
and the observed data is {5, 7, 4}.
(a) Create R vectors to represent a set of possible A values ranging from 0.01 to 100 in steps
of 0.001, and create an R vector to represent a log-uniform prior distribution, where the
probabilities are proportional to 1/A. Normalise the vector of prior probabilities so that it
adds to 1. Hint: This question is the same as 3(d).
(b) Create an R vector representing the likelihood values. You can use dpois () or the given
formula.
(c) Compute and plot the posterior distribution.
(d) Calculate the posterior probability that A is greater than 5.
Transcribed Image Text:Suppose the number of people in a gym each morning has a Poisson distribution, but with the rate parameter/mean A unknown. The probability mass function for the Poisson distribution is given by A exp(-A) p(x|A) = x! (5) and the observed data is {5, 7, 4}. (a) Create R vectors to represent a set of possible A values ranging from 0.01 to 100 in steps of 0.001, and create an R vector to represent a log-uniform prior distribution, where the probabilities are proportional to 1/A. Normalise the vector of prior probabilities so that it adds to 1. Hint: This question is the same as 3(d). (b) Create an R vector representing the likelihood values. You can use dpois () or the given formula. (c) Compute and plot the posterior distribution. (d) Calculate the posterior probability that A is greater than 5.
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