Let \( x, y \) be real numbers satisfying \( y \geq x^2 + 1 \). Prove that there exists a bounded random variable \( Z \) such that

\[

E[Z] = 0, E[Z^2] = 1, E[Z^3] = x, E[Z^4] = y.

\]

Here, \( E \) denotes the expectation.

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