I need math help in calculating the variance, to find variance when given range and mean

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x is a random variable with range (2,3), mean=9/4 what is the variance? I need to know if what the variance is by only having the mean and range. Please help

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You know $1 = p_2 + p_3$ and $9/4 = 2 p_2 + 3 p_3$, so you can figure out that $p_2 = 3/4$. Then it's a matter of computing the variance as $(2 - 9/4)^2p_2 + (3 - 9/4)^2p_3$.