Random variable mean variance (Jee Mains)

Random Variables and Distributions

Hard

Random variable mean variance

A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{{2a + 1}}{{30}},\frac{{8a - 1}}{{30}},\frac{{4a + 1}}{{30}}$ , b respectively, where a, b ∈ R. Let μ and σ respectively be the mean and standard deviation of X such that σ² + μ² = 2. Then $\frac{a}{b}$ is equal to :

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