A random variable X takes values $0,1,2,3$ with probabilities $\frac{2 a+1}{30}, \frac{8 a-1}{30}, \frac{4 a+1}{30}, b$ respectively, where $\mathrm{a}, \mathrm{b} \in \mathrm{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of X such that $\sigma^2+\mu^2=2$. Then $\frac{a}{b}$ is equal to :