Show that two random variables and cannot have a joint normal-gamma distribution such that E()

Question:

Show that two random variables μ and τ cannot have a joint normal-gamma such that E(μ) = 0, Var(μ) = 1, E(τ) = 1/2, and Var(τ ) = 1/4.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...