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If a continuous random variable x has the probability density function

then the value of a such that P[x ≤ a] = P[x > a] is:

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Given

Calculation

P(X < a) = 1/a2 = 

⇒ x2dx = 1/2

⇒ 3[x3/3]a0 = 1/2

⇒ 3 × (a3/3 - 0) = 1/2

⇒ a3 = 1/2

∴ The value of a such that P[x ≤ a] = P[x > a] is (1/2)1/3

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