The expected value is
![E[X]=\displaystyle\sum_xx\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x=\dfrac{0+1+\cdots+9+10}{11}=\dfrac{55}{11}=\boxed{5}](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Csum_xx%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%3D%5Cdfrac%7B0%2B1%2B%5Ccdots%2B9%2B10%7D%7B11%7D%3D%5Cdfrac%7B55%7D%7B11%7D%3D%5Cboxed%7B5%7D)
The standard deviation is the square root of the variance, which is
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
where
![E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x^2=\dfrac{0^2+1^2+\cdots+9^2+10^2}{11}=\dfrac{385}{11}=35](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Csum_xx%5E2%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%5E2%3D%5Cdfrac%7B0%5E2%2B1%5E2%2B%5Ccdots%2B9%5E2%2B10%5E2%7D%7B11%7D%3D%5Cdfrac%7B385%7D%7B11%7D%3D35)
so that
![V[X]=35-5^2=10](https://tex.z-dn.net/?f=V%5BX%5D%3D35-5%5E2%3D10)
making the standard deviation
![\sqrt{V[X]}=\sqrt{10}\approx\boxed{3.16}](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B10%7D%5Capprox%5Cboxed%7B3.16%7D)
Answer:
Step-by-step explanation:
Take out 4 from each term on the left.
4(B^2 - B) = -1 Divide both sides by 4
4(B^2 - B)/4 = - 1/4
(B^2 - B) = -1/4 Add 1/4 to both sides
B^2 - B + 1/4 = - 1/4+1/4
B^2 - B + 1/4 = 0
(b - 1/2)(b - 1/2)
This has 2 equal roots of (b - 1/2)(b - 1/2) or b = 1/2 , b = 1/2.
When that happens, the quadratic just touches the x axis (in this case at 1/2)
I've provided a graph to show you how this happens. None of your choices are what I'm getting. The answer is 1/2 no matter how it is factored.
Answer:
5
Step-by-step explanation:
7-2=x
7-2=5
x=5
.........................
Answer:
Segment DE is half the length of segment AC. -- Substitution property of equality
Step-by-step explanation:
Here is given a proof for proving line joining mid segment is parallel and half the length of third side.
Stepwise proof is given in two columns
We find that for every line there is a justification as
STatement Justification
D and E coordinates found out MId point formula
DE and BC are measured Distance formula
DE=1/2 BC Substitution property of equality
This justification was missing in the given proof and with this included proof would be complete