How to draw the image of Lyl = LXL

How to draw the image of Lyl = LXL

Y = x and y = - X are two intersecting lines

Given the function f (x) = LXL + x ^ 2 (x ∈ R), the analytic expression of the function is written as a piecewise function, and the function image is drawn

f(x)=lxl+x^2
=x²+x(x>=0)
=x²-x(x

It is known that the function f (x) = 1 + lxl-x / 2 (- 2)

Just divide x into (- 2,0) and [0,2]
When - 2 & lt; X & lt; 0, f (x) = 1-x-x / 2 = 1-3x / 2,
When 0 & lt; = x & lt; = 2, f (x) = 1 + x-x / 2 = 1 + X / 2
Draw two images respectively, and the general image is as shown in the figure

If the function y = LXL (1-x) is an increasing function on interval a, then interval a is an increasing function

x

On the problem of cov (x, y) = e (XY) - E (x) e (y)
CoV (x, y) = e (XY) - E (x) e (y), isn't e (XY) = e (x) e (y)?
Are these two e (XY) different?

E=EX+EY

Covariance formula: cov (x, y) = e (XY) - exey, what is the intermediate process? How to multiply e
Why are the middle two terms of E (xy-ex * y-ey * x + ex * ey) = e (XY) - exey left out

COV（X,Y）=E{[X-E（X)][Y-E（Y）]}=E(XY)-E(X)E(Y)-E(Y)E(X)+E(X)E(Y)
=E（XY）-EXEY
I don't know how to ask,

Let the covariance of two-dimensional random variables (x, y) cov (x, y) = 1 / 6 and D (x) = 4, D (y) = 9, then the correlation coefficient between X and Y is

Ρ xy = cov (x, y) / root (DXDY) = 1 / 6 / (3 * 3 / 2) = 1 / 6 * 2 / 9 = 2 / 54 = 1 / 27

The small circle in the upper right corner indicates how to use the symbol,
the sooner the better,

What is the symbol in the middle of the circle
Up and down all the way out
It's also the type symbol of the plastic pipe

Diameter: fai
φ - empty set
A magnetic flux; an angle

How to make such a symbol

∞
is this one?
Insert mathematical symbols in special symbols with word