You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5C%2C%5Cmathrm%20dx%3D710)
and the second moment is
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B1%2C513%2C900%7D3)
The second moment is useful in finding the variance, which is given by
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3](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%3D%5Cdfrac%7B1%2C513%2C900%7D3-710%5E2%3D%5Cdfrac%7B1600%7D3)
You get the standard deviation by taking the square root of the variance, and so
![\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B%5Cdfrac%7B1600%7D3%7D%5Capprox23.09)
Answer:
Step-by-step explanation:
x² - 24x + 5 = 0
x² - 24x = -5
Now divide the co efficient of x by 2 and square the quotient and add to both sides
24/2 = 12
12² = 144. Now add 144 to both sides of the equation.
x² - 24x + 144 = 5 + 144
x² - 24x + 144 = 149
x² - 2*12*x + 12² = 149
(x - 12)² = 149
Both sides take square root
x - 12 = ±√149
x = 12 ± √149
"DJ= DL" is the one statement among the following choices given in the question that is not necessarily true. The correct option among all the options that are given in the question is the fourth option. I hope that this is the answer that you were looking for and it has actually come to your desired help.
<u>THIS ANSWER IS WRONG EVERYBODY</u>
Answer:
Step-by-step explanation:
y2-y1/x2-x1
1+3
3-1
your slope is 4/2 or 2. keep going down to find what y is when x is 0, which happens to be -5
so now you have a slope and a y intercept you can solve like y=mx+b where m is your slope and B is your y intercept
y=2x-5 is your answer
Answer:
30%
Step-by-step explanation:
<u>Key</u><u> </u><u>skills</u><u> </u><u>needed</u><u>:</u><u> </u><u>Probability</u>
1) There is a 70% chance of rain.
2) We need to find the chances against rain.
3) To do this, we need to use the fact that
70% + x = 100% (Since all the probabilities add up to 1 or 100%)
4) If you subtract 70% from both sides, x = 30%
5) This means the probability against rain is 30%.
<em>Hope</em><em> </em><em>you</em><em> </em><em>understood</em><em> </em><em>and</em><em> </em><em>have</em><em> </em><em>a</em><em> </em><em>nice</em><em> </em><em>day</em><em>!</em><em>!</em><em> </em><em>:</em><em>D</em>
