Mathematics, 24.07.2020 06:01 ZachDom4784
Given the probability density function f(x) = 1/5 over the interval [4, 9], find the expected value, the
mean, the variance and the standard deviation.
Expected value:
Mean:
Variance:
Standard Deviation:
![Given the probability density function f(x) = 1/5 over the interval [4, 9], find the expected value](/tpl/images/1708/8771/484e8.jpg)
Answers: 3
![E[X^k] = \int_{4}^{9}x^k f(x) dx](/tpl/images/0712/2935/b1240.png)
![Var(X) = E[X^2}- (E[X])^2](/tpl/images/0712/2935/1ff14.png)
![\sqrt[]{Var(X)}](/tpl/images/0712/2935/9911d.png)
![E[X]](/tpl/images/0712/2935/17992.png)
![E[X] = \int_{4}^{9}\frac{1}{5}dx = \frac{9^2-4^2}{2\cdot 5} = \frac{13}{2}](/tpl/images/0712/2935/fdf9f.png)
![E[X^2] = \int_{4}^{9}\frac{x^2}{5}dx = \frac{9^3-4^3}{3\cdot 5} = \frac{133}{3}](/tpl/images/0712/2935/0a307.png)
![\frac{5}{2\sqrt[]{3}}](/tpl/images/0712/2935/96ec5.png)
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Given the probability density function f(x) = 1/5 over the interval [4, 9], find the expected value,...
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