The weight of milk powder in a 1 kg package is normal(, 2 ) distribution (where

The weight of milk powder in a "1 kg" package is normal(μ, σ²) distribution (where it is known that the mean μ = 1015 g). Let a random sample of 10 packages be taken and weighed. The weights are

(a) What is the equation for the shape of the likelihood function of the variance σ²?
(b) We believe (before looking at the data) that the standard deviation is as likely to be above 5 as it is to be below 5. (Our prior belief is that the distribution of the standard deviation has median 5.) Find the inverse chi-squared prior with 1 degree of freedom that fits our prior belief about the median.
(c) Change the variable from the variance to the standard deviation to
nd the prior distribution for the standard deviation σ.
(d) Find the posterior distribution of the variance σ².
(e) Change the variable from the variance to the standard deviation to find the posterior distribution of the standard deviation.

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