Mathematics, 01.07.2021 16:00 kailiesoto52
The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x < 12 0 otherwise 5-1 Derive the cumulative distribution function F(x) for 6 < x < 12. The answer is a function of x and is NOT 1! Show the antiderivative in your solution. 5-2 What is E(X) = {the mean of all sheet thicknesses)? Show the antiderivative in your solution.
Answers: 1
![$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$](/tpl/images/1387/3613/6d52a.png)
![$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $](/tpl/images/1387/3613/d89fc.png)
![$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$](/tpl/images/1387/3613/6ada6.png)
![$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$](/tpl/images/1387/3613/01262.png)
![$=\frac{1}{450} [4608 - 252]$](/tpl/images/1387/3613/58e8c.png)
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