Mathematics, 24.07.2020 06:01, woodpeckerdeejpe8wvh
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answers: 3
![E[X^k] = \int_{4}^{7}x^k f(x) dx](/tpl/images/0712/2886/d4c82.png)
![Var(X) = E[X^2]- (E[X])^2](/tpl/images/0712/2886/64682.png)
![\sqrt[]{Var(X)}](/tpl/images/0712/2886/9911d.png)
![E[X]](/tpl/images/0712/2886/17992.png)
![E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}](/tpl/images/0712/2886/ee182.png)
![E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31](/tpl/images/0712/2886/71392.png)
![\frac{\sqrt[]{3}}{2}](/tpl/images/0712/2886/ae5e3.png)
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