  Privacy protection with synthetic data generation often uses differentially
private statistics and model parameters to quantitatively express theoretical
security. However, these methods do not take into account privacy protection
due to the randomness of data generation. In this paper, we theoretically
evaluate R\'{e}nyi differential privacy of the randomness in data generation of
a synthetic data generation method that uses the mean vector and the covariance
matrix of an original dataset. Specifically, for a fixed $\alpha > 1$, we show
the condition of $\varepsilon$ such that the synthetic data generation
satisfies $(\alpha, \varepsilon)$-R\'{e}nyi differential privacy under a
bounded neighboring condition and an unbounded neighboring condition,
respectively. In particular, under the unbounded condition, when the size of
the original dataset and synthetic datase is 10 million, the mechanism
satisfies $(4, 0.576)$-R\'{e}nyi differential privacy. We also show that when
we translate it into the traditional $(\varepsilon, \delta)$-differential
privacy, the mechanism satisfies $(4.00, 10^{-10})$-differential privacy.
