![\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5CBbb%20E%5B%284X%20-%202%29%5E2%5D)
so by definition of expectation,
![\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5Cdisplaystyle%20%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20%284x-2%29%5E2%20f_X%28x%29%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%203%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Integrate by parts (twice).
First, let
so that
![\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%20-%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Next,
so that
![\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac13%20%284x-2%29%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%20%5Cfrac43%20%5Cint_0%5E%5Cinfty%20e%5E%7B-3x%7D%20%5C%2C%20dx%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac23%20-%20%5Cfrac49%20e%5E%7B-3x%7D%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20-%20%5Cfrac%7B16%7D3%20%2B%20%5Cfrac%7B32%7D9%20%3D%20%5Cboxed%7B%5Cfrac%7B20%7D9%7D)
Answer:
about 9 seconds
Step-by-step explanation:
18x60/108
.............................................your answer is 16
We use the distance formula for this problem.
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The distance between point (-2,-2) and point (-2,4).
d = √[(⁻2 - ⁻2)² + (4 - ⁻2)²] = 6 units
Then, compute for 20% of 6 units:
Distance traveled = 6(0.2) = 1.2 units
Use 1.2 units as distance and the starting point (-2,-2). The x-coordinate should still be at -2 because the distance is a straight line as shown in the picture.
1.2 = √[(-2 - ⁻2)² + (y - ⁻2)²]
Solving for y,
y = -0.8
The point is found at (-2,-0.8). This is located at quadrant 3. As to the distance traveled, that would be: 1.2*6 = 6 miles. Thus, the answer is C.
Answer:
A.1 Exercise
2. Reduce the intake of salt
3. Reduce intake of fatty foods
4. Eating well balance diet
B.1. Regular exercise
2. Avoid smoking
3. Avoid excessive intake of alcohol
4. Reduce intake of cholesterol
