Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean and unknown precision ,

Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean μ and unknown precision τ , and also that the joint prior distribution of μ and τ is the normal-gamma distribution satisfying the following conditions: E(μ) = 0, E(τ ) = 2, E(τ2) = 5, and Pr(|μ| < 1.412) = 0.5. Determine the prior hyperparameters μ0, λ0, α0, and β0.