Answer:
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Step-by-step explanation:
Given
![\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccc%7Dx%20%26%20%7B0%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%26%20%7B5%7D%20%5C%20%5C%5C%20P%28x%29%20%26%20%7B0.2%7D%20%26%20%7B0.1%7D%20%26%20%7B0.1%7D%20%26%20%7B0.2%7D%20%26%20%7B0.2%7D%26%20%7B0.2%7D%20%5C%20%5Cend%7Barray%7D)
Required
The standard deviation
First, calculate the expected value E(x)
![E(x) = \sum x * P(x)](https://tex.z-dn.net/?f=E%28x%29%20%3D%20%5Csum%20x%20%2A%20P%28x%29)
So, we have:
![E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2](https://tex.z-dn.net/?f=E%28x%29%20%3D%200%20%2A%200.2%20%2B%201%20%2A%200.1%20%2B%202%20%2A%200.1%20%2B%203%20%2A%200.2%20%2B%204%20%2A%200.2%20%2B%205%20%20%2A%200.2)
![E(x) = 2.7](https://tex.z-dn.net/?f=E%28x%29%20%3D%202.7)
Next, calculate E(x^2)
![E(x^2) = \sum x^2 * P(x)](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%20%5Csum%20x%5E2%20%2A%20P%28x%29)
So, we have:
![E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%200%5E2%20%2A%200.2%20%2B%201%5E2%20%2A%200.1%20%2B%202%5E2%20%2A%200.1%20%2B%203%5E2%20%2A%200.2%20%2B%204%5E2%20%2A%200.2%20%2B%205%5E2%20%20%2A%200.2)
![E(x^2) = 10.5](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%2010.5)
The standard deviation is:
![\sigma = \sqrt{E(x^2) - (E(x))^2}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7BE%28x%5E2%29%20-%20%28E%28x%29%29%5E2%7D)
![\sigma = \sqrt{10.5 - 2.7^2}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B10.5%20-%202.7%5E2%7D)
![\sigma = \sqrt{10.5 - 7.29}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B10.5%20-%207.29%7D)
![\sigma = \sqrt{3.21}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B3.21%7D)
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<em> --- approximated</em>
26.15,because your suppose to divide to see how many coins you have for each category and that’s how u get 26.15 u divide 51 by 1.95 !
Answer:
the difference is 5
Step-by-step explanation:
difference means subtraction meaning you subtract 15-10 and your answer would be 5 <em>your welcome</em>
13 x 6 = 78 it cant be multiplied anymore so it can go into 80 about 6 times.
amount after 2 years = 6000(1 + (0.04/12))^24 = 6498.86