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For the following probability density fu...

For the following probability density function (p.d.f) of X find : (i) P ` (X lt 1) , (ii) p (|X| lt 1)` if ` f(x) = (x^(2))/(18') - 3 lt x lt 3 `, f(x) = 0 , otherwise

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(i) ` p(Xlt 1) = int_(-3)^(1) f(x) =int_(-3)^(1) (x^(2))/(18) = (1)/(18) [(x^(3))/(3)]_(-3)^(1)`
` = (1)/(54) [ 1 + 27 ] = (28)/(54) = (14)/(27)`
(ii) ` P |X| lt 1 = P (-1 lt x lt 1) `
`= int_(-1)^(1) f(x) dx = int_(-1)^(1) (x^(2))/(18) dx `
` = (1)/(18) [(x^(3))/(3)]_(-1)^(1) = (1)/(54) [ 1 + 1] `
` (2)/(54) = (1)/(27)`
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