Exercise6.1 Assume that Y f (y) and apriori (). Afterobtainingthefirstobservation y1 from f (y)

Exercise6.1 Assume that Y ∼ fθ (y) and apriori θ ∼ π(θ). Afterobtainingthefirstobservation y1 from fθ (y) we updatethedistributionof θ by calculatingitsposteriordistribution π(θ|y1) and use itasapriordistributionfor θ before weobserve y2 independent of y1. Having y2, weupdatethe distributionof θ againbyderivingthecorrespondingposteriordistribution.Showthatonewillget the sameposteriordistributionof θ if insteadofcalculatingitsequentially,hewouldusetheentire data (i.e. y1 and y2) andtheoriginalprior π(θ).