Suppose that two random variables and have the joint normal-gamma distribution such that E() = 5. Var() = 1, E( ) = 1/2,

Suppose that two random variables μ and τ have the joint normal-gamma distribution such that E(μ) = −5. Var(μ) = 1, E(τ ) = 1/2, and Var(τ ) = 1/8. Find the prior hyperparameters μ0, λ0, α0, and β0 that specify the normal-gamma distribution.