Alliyus Caesar

PERSONAL ACCOUNT

[Alliyus Caesar @caesar_alliyus]

@asherrkiinee .

[Alliyus Caesar @caesar_alliyus]

World health organization.

[BNO News @BNOFeed]

BREAKING: WHO says hantavirus outbreak on cruise ship likely involves human-to-human transmission

[Alliyus Caesar @caesar_alliyus]

@RapidResponse47 😂

[Alliyus Caesar @caesar_alliyus]

"golden age"

[Al Jazeera English @AJEnglish]

President Trump says the US will help manage “traffic buildup” in the Strait of Hormuz, adding “big money will be made” and that Iran can begin reconstruction.

Under the ceasefire, Iran will collect transit fees to fund rebuilding.

🔴 LIVE updates: https://t.co/9YvbvxfUvc

[Alliyus Caesar @caesar_alliyus]

Rescued by "WHOM" ?

[Insider Wire @InsiderWire]

#BREAKING: One of the U.S. F-15 fighter jet pilots was successfully rescued.

[Alliyus Caesar @caesar_alliyus]

@Emmanuel_Tips ╱◥██████◣
│∩│🌄▤│▤▤│

[Alliyus Caesar @caesar_alliyus]

How they do this. This is so terrifying 😭

[Parody Jeff @Parodyjeffx]

𝗕𝗥𝗘𝗔𝗞𝗜𝗡𝗚🚨⚡️
Israeli settlers in the West Bank terrorized a Palestinian child waiting for his father in a car.

They reached in and splashed white construction paint all over him before leaving.

[Alliyus Caesar @caesar_alliyus]

Can't be humans.

[BBC News (World) @BBCWorld]

Israeli forces kill Palestinian couple and two of their children in occupied West Bank https://t.co/m5llYcCo6l

[Kishan🆒 @Kishann108]

Unpopular opinion:

Shoes are not meant for hot and humid countries like India, where the temperature stays above 35°C most of the time.

Wearing them during summers is idiotic and illogical.

[Alliyus Caesar @caesar_alliyus]

Allow?

[Treasury Secretary Scott Bessent @SecScottBessent]

President Trump’s energy agenda has resulted in oil and gas production reaching the highest levels ever recorded.

To enable oil to keep flowing into the global market, the Treasury Department is issuing a temporary 30-day waiver to allow Indian refiners to purchase Russian oil. This deliberately short-term measure will not provide significant financial benefit to the Russian government as it only authorizes transactions involving oil already stranded at sea.

India is an essential partner of the United States, and we fully anticipate that New Delhi will ramp up purchases of U.S. oil. This stop-gap measure will alleviate pressure caused by Iran’s attempt to take global energy hostage.

[Alliyus Caesar @caesar_alliyus]

@Coinvo Why we have to do this?

[Alliyus Caesar @caesar_alliyus]

@jimNjue_ @grok is it true

[Bask @baskgod]

They bombed Iran just in case Iran bombed them? And are now scared Iran might bomb them back? Am I reading this correct

[Alliyus Caesar @caesar_alliyus]

@Liza_Coder AI

[Alliyus Caesar @caesar_alliyus]

"buy more farm land"

[Claude @claudeai]

We've also created plugins across HR, design, engineering, ops, financial analysis, investment banking, equity research, private equity, and wealth management to help users see what's possible and start building their own.

[fatima saleh @Phatymarh44]

7 Haram Things Parents Do with Their Kids

1. Slapping on their Faces – The Prophet ﷺ forbade striking the face, as it is the most honourable part of the body.
2. Having a Favourite Child – Showing favouritism creates jealousy and injustice among siblings.
3. Forcing them to get married – Islam gives children the right to choose their spouse; compulsion is oppression.
4. Teaching them Haram Things – Parents are guardians; guiding towards sin is a betrayal of trust.
5. Comparing their Child with Others – Such comparisons break confidence and plant resentment in the heart.
6. Neglecting their Child’s Islamic Education and Upbringing – The greatest responsibility of parents is to nurture their children upon Deen.
7. Disrespecting their Child in Front of Others – Public humiliation wounds the soul and destroys mutual love and respect.

Parents are a child’s first teachers. Their actions shape not just the dunya life of the child but also their akhirah.

[adam @AdameMedia]

Epstein survivor: “I was raped three times a day and I wasn’t the only girl. It was a conveyor belt of abuse.”

We are ruled by the monsters behind this.

The entire system needs to be destroyed.

[Alliyus Caesar @caesar_alliyus]

@AdameMedia And she was "10 years" old

[vixhaℓ @TheVixhal]

I found out my girlfriend cheated on me. Instead of breaking up right away, I made a fake account, sent her the proof anonymously, and told her that if she didn’t send me money, I’d tell her boyfriend everything.

I shared this whole plan with my best friend for advice, but this mf went behind my back and shared everything with my girlfriend.

When confronted, he said
Why does it matter? I thought she deserved to know.

He wasn’t just betraying me. He was behaving like a random variable after you marginalize out all the hidden information.

In probability, to understand what you actually know, you marginalize over hidden variables.

That means you sum over all the possibilities you can’t observe to compute the probability of what you can observe.

Marginal probability is a statistical measure that represents the probability of a single event by aggregating over all possible values of other variables.

Formula
P(A) = Σ P(A, Bi)

Where
P(A) = Marginal probability of event A
P(A, Bi) = Joint probability of A and B
Σ = Summation

Let's take an example and solve step by step

A dating app wants to find the probability of users sending messages, regardless of whether they get a response. The data shows message sent vs response received:

Short forms
- M = Message
- R = Response

Joint Probability Table
- M (Yes), R (Yes) = 0.30
- M (Yes), R (No) = 0.25
- M (No), R (Yes) = 0.10
- M (No), R (No) = 0.35

Step 1 What we want to marginalize
- We want P(M = Yes)

Step 2 Joint probabilities for M = Yes
- P(M = Yes, R = Yes) = 0.30
- P(M = Yes, R = No) = 0.25

Step 3 Apply marginal probability
- P(M = Yes)
- P(M=Yes, R=Yes) + P(M=Yes, R=No)
- 0.30 + 0.25 = 0.55

P(Message = Yes) = 0.55

Final Answer
The marginal probability of a user sending a message is 0.55 or 55%, regardless of whether they receive a response.

Congratulations, you've just learned Marginal Probability.

Bonus: Applications in AI/ML

1. Bayesian Networks:
Computing marginal probabilities by summing out irrelevant variables to make predictions and inferences in graphical models.

2. Latent Variable Models:
In topic modeling (LDA) and hidden Markov models, marginalizing over hidden states to find the probability of observed data.

3. Feature Selection:
Identifying which features independently correlate with target variables by computing marginal distributions, helping reduce dimensionality.

4. Probabilistic Classification:
Naive Bayes classifiers use marginal probabilities of features to classify data, assuming independence between features.