Question

Find E(x) for the Probability density over the interval [1,3]

1 f(x) = x, over the interval [1,3]. Find E(x). O A. O B. O C. O D. 513 26 15 9 - 5 1 - 2

Answer 1

`\displaystyle E(x)=(26)/(3)`

Explanation:

`\displaystyle E(x)=\int^b_axf(x)dx\\\\E(x)=\int^3_1x^2dx\\\\E(x)=(x^3)/(3)\biggr|^3_1\\\\E(x)=(3^3)/(3)-(1^3)/(3)\\\\E(x)=(27)/(3)-(1)/(3)\\\\E(x)=(26)/(3)`