Notice that 
for 
implies that 
elsewhere, since
where 
is a random variable representing cable lengths according to the PDF 
.
a. By definition of expectation, the mean is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x\,\mathrm dx=1205](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf%28x%29%5C%2C%5Cmathrm%20dx%3D0.1%5Cint_%7B1200%7D%5E%7B1210%7Dx%5C%2C%5Cmathrm%20dx%3D1205)
The variance is
![\operatorname{Var}[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=%5Coperatorname%7BVar%7D%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
where
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x^2\,\mathrm dx=\frac{4,356,100}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf%28x%29%5C%2C%5Cmathrm%20dx%3D0.1%5Cint_%7B1200%7D%5E%7B1210%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B4%2C356%2C100%7D3)
so that the variance is 
, making the standard deviation 
.
b. The proportion of cables within specs is
I think you miss types your question
Answer:
132 is the answer
Step-by-step explanation:
324x80=25920 if you put them on top of each other like so...
324
x80
____
25920
Alright, since after the second term, the pattern is consistent, we will be using the 3rd and 2nd terms in the formula, instead of the 2nd and 1st.
1. divide the 3rd term by the second term. 45/15=3
2. Check the pattern by applying this method to the 4th and 3rd terms. 135/45=3 This means is is in fact G.S.
3. Now we go back to the traditional formula, which would be 1st term*r^n-1
4. Work it out. The r in the formula represents the 3, which we worked out. The n in the formula represents the term your trying to find. 15*3^6-1=3645
Your answer for the 6th term should indeed be 3645, which may sound odd, but it's right.
~Hope this helps!
