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Analytical and Computational Approach

This paper focuses on an analytical and computational approach to problem-solving in various industries.

Violet Stevens
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Analytical and Computational Approach3. fx(x) = (theta^2 + theta) x^(theta-1) (1-x);0<x<1;theta > 0a. Consider,𝐸(𝑋)=∫π‘₯𝑓(π‘₯)𝑑π‘₯10=∫π‘₯(π‘‘β„Žπ‘’π‘‘π‘Ž2+π‘‘β„Žπ‘’π‘‘π‘Ž)π‘₯π‘‘β„Žπ‘’π‘‘π‘Žβˆ’1(1βˆ’π‘₯)𝑑π‘₯10=(π‘‘β„Žπ‘’π‘‘π‘Ž2+π‘‘β„Žπ‘’π‘‘π‘Ž)∫π‘₯π‘‘β„Žπ‘’π‘‘π‘Ž(1βˆ’π‘₯)𝑑π‘₯10=(π‘‘β„Žπ‘’π‘‘π‘Ž2+π‘‘β„Žπ‘’π‘‘π‘Ž)∫π‘₯π‘‘β„Žπ‘’π‘‘π‘Žβˆ’π‘₯π‘‘β„Žπ‘’π‘‘π‘Ž+1𝑑π‘₯10=(π‘‘β„Žπ‘’π‘‘π‘Ž2+π‘‘β„Žπ‘’π‘‘π‘Ž)(π‘₯π‘‘β„Žπ‘’π‘‘π‘Ž+1π‘‘β„Žπ‘’π‘‘π‘Ž+1βˆ’π‘₯π‘‘β„Žπ‘’π‘‘π‘Ž+2π‘‘β„Žπ‘’π‘‘π‘Ž+2)01=(π‘‘β„Žπ‘’π‘‘π‘Ž2+π‘‘β„Žπ‘’π‘‘π‘Ž)βˆ—(1π‘‘β„Žπ‘’π‘‘π‘Ž+1βˆ’1π‘‘β„Žπ‘’π‘‘π‘Ž+2)=π‘‘β„Žπ‘’π‘‘π‘Žβˆ—(1+π‘‘β„Žπ‘’π‘‘π‘Ž)βˆ—(1(π‘‘β„Žπ‘’π‘‘π‘Ž+1)βˆ—(π‘‘β„Žπ‘’π‘‘π‘Ž+2))=π‘‘β„Žπ‘’π‘‘π‘Žπ‘‘β„Žπ‘’π‘‘π‘Ž+2thus,π‘‹π‘π‘Žπ‘Ÿβˆ—(π‘‘β„Žπ‘’π‘‘π‘Ž+2)=π‘‘β„Žπ‘’π‘‘π‘Žπ‘‹π‘π‘Žπ‘Ÿβˆ—π‘‘β„Žπ‘’π‘‘π‘Ž+(2βˆ—π‘‹π‘π‘Žπ‘Ÿ)βˆ’π‘‡β„Žπ‘’π‘‘π‘Ž=0π‘‘β„Žπ‘’π‘‘π‘Ž(π‘‹π‘π‘Žπ‘Ÿβˆ’1)=βˆ’2π‘‹π‘π‘Žπ‘Ÿπ‘‘β„Žπ‘’π‘‘π‘Ž=βˆ’2βˆ—π‘‹π‘π‘Žπ‘Ÿ(π‘‹π‘π‘Žπ‘Ÿβˆ’1)

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