If the probability density function of a random variable X is f ( x ) = 2 x in 0 ≤ x ≤ 2 , then P ( X 1.5 ∣ X 1 ) is equal to

Question

If the probability density function of a random variable X is f ( x ) = 2 x ​ in 0 ≤ x ≤ 2 , then P ( X > 1.5 ∣ X > 1 ) is equal to

TestHub · Accepted Answer

∫ 1.5 2 ​ f ( x ) dx , where f ( x ) = 2 x ​ ∫ 1.5 2 ​ 2 x ​ d x = 2 1 ​ ⋅ ∫ 1.5 2 ​ x d x = 2 1 ​ [ 2 x 2 ​ ] 1.5 2 ​ = 4 1 ​ [ 4 − 2.25 ] = 4 1 ​ × [ 1.75 ] = 400 175 ​ = 16 7 ​ ​

Mathematics - Application of Derivative Question with Solution | TestHub

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