Assume that Y1, ..., Yn are IID normal random variables with mean 0 and variance σ 2 . Thus, the PDF for any Yi is given by: p(y|σ 2 ) = 1 √ 2πσ exp [− y 2 2σ 2 ]. A conjugate prior for σ 2 is an inverse-gamma distribution. That is, an inverse-gamma distribution with parameters α and β is given by: p(σ 2 ) = β α Γ(α) (1/σ2 ) α+1 exp [−β/σ2 ]. (Note that σ 2 > 0.) Complete the following: • Derive the posterior distribution for σ 2 assuming n IID normal data points in a sample and an inversegamma prior, as above. You should find that the posterior distribution is also an inverse-gamma distribution. What are the parameters of