Word Count : 426

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The probability distribution function is given as: [ p(x) = \begin{cases} 3N(x^2 - 1) & 1 < x < 2 \ 0 & \text{elsewhere} \end{cases} ] Step 1: Find the normalization constant (N) The normalization condition is: [ \int_{-\infty}^{\infty} p(x) , dx = 1 ] Since (p(x) = 0) outside (1 < x < 2), [ \int_1^2 3N(x^2 - 1) , dx = 1 ] Compute the integral: [ \int_1^2 (x^2 - 1) , dx = \int_1^2 x^2 , dx - \int_1^2 1 , dx ________ _________ ______ _______ _____ ___ ______ ___ ________ ______.
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