Probability · Mean and variance of distribution

A random variable

X

takes values 0, 1, 2, 3 with probabilities

\dfrac{2a+1}{30}, \dfrac{8a-1}{30}, \dfrac{4a+1}{30}

b

respectively, where

a, b \in \mathbb{R}

. Let

\mu

and

\sigma

respectively be the mean and standard deviation of

X

such that

\sigma^2 + \mu^2 = 2

. Then

\dfrac{a}{b}

is equal to:

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