## Probability inequality of an average in terms of individual probabilities

Let $$X_1, cdots, X_n$$ be identically distributed non-negative real-valued random variables that are not necessarily independent. Note that we have trivially for everything $$varepsilon> 0$$:

$$mathbb {P} left { frac {1} {n} sum_ {i = 1} ^ {n} X_i geq varepsilon right } leq sum_ {i = 1} ^ { n} mathbb {P} {X_i geq varepsilon } = n mathbb {P} {X_1 geq varepsilon }.$$

For $$n geq 3$$, is there still an example where the above inequality holds for equality, or can we get a sharper bound for $$n$$? I am particularly interested in the framework where $$n$$ is wide.

For $$n = 2$$, the example $$X_1, X_2 sim U [0,1]$$ with $$X_2 = 1 – X_1$$ and $$varepsilon = 0.5$$ presents an example where inequality is about equality, but it seems difficult to generalize to $$n> 2$$.

## usability tests – In-depth individual interviews vs co-design workshop

In my current project, we have planned a usability test component using the method of in-depth individual interviews (IDI).

Due to unforeseen circumstances, the project must be delayed. I wonder if we can replace a co-design workshop rather than IDI because we do not want to extend the time further.

Here are my considerations:

Usage tests

• We have around 4-5 modules which require different participants
• In total, we will have to test with about 20-25 participants
• It will take at least a month to complete it
• However, IDIs will help us to identify navigation issues as well as mismatched interface issues

Co-conception workshop

• We will bring together at least 5 users of each module (each 1 session module)
• At most, it will take less than 2 weeks
• We will print the designed wireframes and paste them in the room and bring users to discuss / work on them to validate the content
• However, users will not be able to navigate the system, so I am concerned that we may experience usability issues. But they are able to validate the content (for example, form fields, information, statuses, etc.)

Let me know if it is a good idea / possible to make such arrangements. Thank you!

## How do you calculate the contribution of each individual number to the product?

If you have four digits, say `1.1, 1.02, 0.98, 1.8` and the product of these are `1.979208`, how do you standardize the contribution of each individual number to the product?

In case of addition, the sum is `4.9` so the contributions would
``` 22.4% 20.8% 20.0% 36.7%```

Calculated as (for example)

`1.1/4.9 = 22.4%`

I hope that the contribution of `0.98` should have a negative contribution on the product, just like a negative number on the sum.

## wordpress – Some individual posts do not open correctly in a WP on AWS Lighsail

I have a `WordPress` no `Lightsail` of `AWS` with many messages, some messages do not open properly, it does not load auxiliary files like Images, `CSS` and `JS`, I discovered that it extracts these files from the machine's IP on the `AWS` and not from the domain, the ip does not have an SSL certificate and the files do not load because they are not secure. If I change the permanent link of the defective message, it opens normally, and if I try to access the message on the old permanent link, it does not give an error message not found, it opens again without external files.

I have a cache plugin installed `WP Fastest Cache`.

Anyone have any ideas or has there been a tip?

## root access – Individual commands work fine, but shell script generates errors

I am trying to create a shell script to configure iptables and add some routes to my device running Android 10. I have root access.

Here is the script. I called him `script.sh`:

``````#!/system/bin/sh
iptables -t filter -F FORWARD
iptables -t nat -F POSTROUTING
iptables -t filter -I FORWARD -j ACCEPT
iptables -t nat -I POSTROUTING -j MASQUERADE
ip rule add from 192.168.43.0/24 lookup 61

sysctl -w net.ipv6.conf.wlan1.disable_ipv6=1
``````

I have a root console open via ADB, and I can execute each individual command from the script manually in the console, as follows:

… etc.

But this happens when I run my script:

and I don't really understand why.

I have limited skills with Android and Linux, so I tried to follow and combine a few examples, but I was unlucky.
https://www.pctips4u.com/2016/03/writing-shell-scripts-in-android.html
https://gist.github.com/LouWii/9626480

## Can noindex tags on individual articles affect global SEO or ranking on Google?

Some SEO gurus promise that noindex attributes are good for devaluing unimportant pages. But when I asked in the Q&A moz, they are quite sure that most of the noindex article on the website can hurt the overall SEO ranking. What is your opinion on this.

## game design – How to make the enemy appear in individual rows, by scrolling down the screen [using 2D DirectX,C]

I am a beginner in game development and I just started creating one 6 months ago. I'm creating a top-down 2D scrolling shooter using DirectX9 and C language. (I know it's an old one to use but I don't have a choice because it's a school project).

The result I want:

• Enemies will be paraded in endless rows from the top to the end of the screen

The problem I have:

Currently, I have managed to spawn enemies in a single row. I don't know how to cut them and sort them into 8 enemies in each row. I really need to know how to sort this out and I hope someone will help me understand this !!

## Google sheets – on the edit script for time stamping on multiple columns with individual time stamp based on the time of the change made, all having the same time stamp

I have checkboxes for all the other columns starting with column C and I want the date stamp to appear in column d of row 2. The script works fine for this, but I also have need to be for column e (check box) Column f Fills a date timestamp; column g (checkbox) column h fills the date timestamp. Originally, I found this to stop the automatic updating that Google's sheets do every day. Any help would be greatly appreciated!

``````function onEdit3() {
var r = s.getActiveCell();
if( r.getColumn() != 8 )
{
var row = r.getRow();
var time = new Date();
time = Utilities.formatDate(time, "GMT+05:30", "dd/MM/yyyy, hh:mm:ss");