2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with th...
2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with that. What he wants to learn more about is the precision of X, which is the inverse of the variance. Bjorn thinks that the precision has a Gamma distribution as described below. Help Bjorn out by finding the posterior distribution for the percision. As we said above, Xi ~ Normal(μ-: 0, σ2)LE 1,.., n, where μ įs known to equal zero, the variance σ2 is unknown and the X's are iid. Therefore, the pdf for X is: The prior distribution fori ~Gamma(w,v). Therefore, the prior distribution can be written as: Find the posterior distribution of (which is probability distribution that you know) given the X where i is in 1 to n being sure to specify the parameters. Show all steps so that Bjorn can follow along.
2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with that. What he wants to learn more about is the precision of X, which is the inverse of the variance. Bjorn thinks that the precision has a Gamma distribution as described below. Help Bjorn out by finding the posterior distribution for the percision. As we said above, Xi ~ Normal(μ-: 0, σ2)LE 1,.., n, where μ įs known to equal zero, the variance σ2 is unknown and the X's are iid. Therefore, the pdf for X is: The prior distribution fori ~Gamma(w,v). Therefore, the prior distribution can be written as: Find the posterior distribution of (which is probability distribution that you know) given the X where i is in 1 to n being sure to specify the parameters. Show all steps so that Bjorn can follow along.