
Recall that the PDF is given by the derivative of the CDF:

The mean is given by
![\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\int_0^2\left(x-\dfrac{x^2}2\right)\,\mathrm dx=\frac23](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_0%5E2%5Cleft%28x-%5Cdfrac%7Bx%5E2%7D2%5Cright%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac23)
The median is the number

such that

. We have

but both roots can't be medians. As a matter of fact, the median must satisfy

, so we take the solution with the negative root. So

is the median.
Answer:
The height of the right trapezoid is 
Step-by-step explanation:
Let
x ----> the height of the right trapezoid in units
we know that
The perimeter of the figure is equal to
we have

---> because is a square
substitute
-----> equation A
<em>In the right triangle CDH</em>


so
Remember that 




so


substitute the values in the equation A
-----> equation A




![6=x[5+\sqrt{3}]](https://tex.z-dn.net/?f=6%3Dx%5B5%2B%5Csqrt%7B3%7D%5D)

The angle RAT which is made with AR and AT line and shown in the figure of protector, measures 30 degrees.
<h3>How to measure the angle in protector?</h3>
Protector is the most useful device to measure the angle between two lines. To measure the angle between two lines using the protector following steps is followed:
- Place the protector center point at the vertex of unknown angle.
- One side of angle should be place at 0 mark line of this device.
- Other side of angle will be equal to the angle shown in protector on that line.
In the given figure, The angle Between AR and AT line is 30 degrees shown in protector.
Thus, the angle RAT which is made with AR and AT line and shown in the figure of protector, measures 30 degrees.
Learn more about the protector here:
brainly.com/question/1161640
#SPJ1