2e8a8cd3-1588-4911-a54d-820d16021d7d
prompter
E(XY) = E(X) E(Y) if X and Y are independet. What about E(X+Y) ?
40800802-d97b-4fe0-87cf-809ac0304abf
2e8a8cd3-1588-4911-a54d-820d16021d7d
assistant
The formula E(XY) = E(X) E(Y) holds true only when X and Y are independent random variables. However, when it comes to finding the expected value of X + Y, we cannot apply the same formula because the sum of two random variables is not necessarily independent.

To calculate E(X+Y), we need to use a different approach. We can use the linearity property of expected values, which states that:

E(aX + bY) = aE(X) + bE(Y)

where a and b are constants.

Using this property, we can rewrite X+Y as 1*X + 1*Y and apply the formula:

E(X+Y) = 1*E(X) + 1*E(Y)

Therefore, the expected value of X+Y is simply the sum of their individual expected values.
0c80a909-0dc3-4ca8-bfdd-df1869c7c180
40800802-d97b-4fe0-87cf-809ac0304abf
prompter
Give me a random base16 colorscheme
2cc8edeb-62b4-4947-85c5-5ad24571d4a7
0c80a909-0dc3-4ca8-bfdd-df1869c7c180
assistant
Sure! Here's a random base16 color scheme:

Background: #2d2d2d
Foreground: #d0d0d0

Black: #1a1a1a
Red: #f4005f
Green: #98e024
Yellow: #fa8419
Blue: #9d65ff
Magenta: #f4005f
Cyan: #58d1eb
White: #e6e6e6

Bright Black: #535353
Bright Red: #f4005f
Bright Green: #98e024
Bright Yellow: #fa8419
Bright Blue: #9d65ff
Bright Magenta: #f4005f
Bright Cyan: #58d1eb
Bright White: #ffffff