A random variable X takes values 0, 1, 2, 3 with probabilities (2 a +1)/30, (8 a -1)/30, (4 a +1)/30, b respectively, where a, b ∈ R. Let μ and σ…

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