Analytical and Computational Approach3. fx(x) = (theta^2 + theta) x^(theta-1) (1-x);0<x<1;theta > 0a. Consider,𝐸(𝑋)=∫𝑥𝑓(𝑥)𝑑𝑥10=∫𝑥(𝑡ℎ𝑒𝑡𝑎2+𝑡ℎ𝑒𝑡𝑎)𝑥𝑡ℎ𝑒𝑡𝑎−1(1−𝑥)𝑑𝑥10=(𝑡ℎ𝑒𝑡𝑎2+𝑡ℎ𝑒𝑡𝑎)∫𝑥𝑡ℎ𝑒𝑡𝑎(1−𝑥)𝑑𝑥10=(𝑡ℎ𝑒𝑡𝑎2+𝑡ℎ𝑒𝑡𝑎)∫𝑥𝑡ℎ𝑒𝑡𝑎−𝑥𝑡ℎ𝑒𝑡𝑎+1𝑑𝑥10=(𝑡ℎ𝑒𝑡𝑎2+𝑡ℎ𝑒𝑡𝑎)(𝑥𝑡ℎ𝑒𝑡𝑎+1𝑡ℎ𝑒𝑡𝑎+1−𝑥𝑡ℎ𝑒𝑡𝑎+2𝑡ℎ𝑒𝑡𝑎+2)01=(𝑡ℎ𝑒𝑡𝑎2+𝑡ℎ𝑒𝑡𝑎)∗(1𝑡ℎ𝑒𝑡𝑎+1−1𝑡ℎ𝑒𝑡𝑎+2)=𝑡ℎ𝑒𝑡𝑎∗(1+𝑡ℎ𝑒𝑡𝑎)∗(1(𝑡ℎ𝑒𝑡𝑎+1)∗(𝑡ℎ𝑒𝑡𝑎+2))=𝑡ℎ𝑒𝑡𝑎𝑡ℎ𝑒𝑡𝑎+2thus,𝑋𝑏𝑎𝑟∗(𝑡ℎ𝑒𝑡𝑎+2)=𝑡ℎ𝑒𝑡𝑎𝑋𝑏𝑎𝑟∗𝑡ℎ𝑒𝑡𝑎+(2∗𝑋𝑏𝑎𝑟)−𝑇ℎ𝑒𝑡𝑎=0𝑡ℎ𝑒𝑡𝑎(𝑋𝑏𝑎𝑟−1)=−2𝑋𝑏𝑎𝑟𝑡ℎ𝑒𝑡𝑎=−2∗𝑋𝑏𝑎𝑟(𝑋𝑏𝑎𝑟−1)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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Mathematics