ramzy0304

Yessir

[4:44 @leliibaby]

every real nigga tried to make a song atleast once in their life

[KUTT THROAT⚔️ @Gatsoxo]

Niggas have fun with their money then want to borrow yours for important stuff

[✶ @echoesofworld]

Lake Como, Italy

[Interesting things @awkwardgoogle]

man buys ps5, store staff celebrate like it's their own, proving men are simple

[EMDG @EmanDaGoon]

Beautiful ❤️

[👤🏴󠁧󠁢󠁥󠁮󠁧󠁿🇫🇷 @1of1pd]

BUKAYO SAKA PREMIER LEAGUE CHAMPIONNNN

[Arsenal @Arsenal]

We did it, together.

[autist @litteralyme0]

-Life of a 2000 born
-Pandemic at the age of enjoyment
-Ai implementation at the age of employment

[🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀 @fuckin_clover]

Rt for good luck 🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀 🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀 🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀 🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀 🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀🍀

[eigenron @eigenron]

your brain is the most neuroplastic in the first 60 mins after waking up. do what you will with that information.

[ramzy0304 @fifj4brf]

@zitha_trevor @Solphendukaa Fair

[ramzy0304 @fifj4brf]

@TheAthleticFC Wasn't the match supposed to be forfeited after they walked off the pitch?

[ramzy0304 @fifj4brf]

@JulianBeccari @TrungTPhan Was it luck or were you using math and probability to win?

[ramzy0304 @fifj4brf]

@JulianBeccari @TrungTPhan Well at least you're not donating your money just like myself

[ramzy0304 @fifj4brf]

@JulianBeccari @TrungTPhan So you no longer gamble?

[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.

[Dr SHRADDHEY KATIYAR @Wegiveyouhealt1]

After a certain age, your parents slowly become your children.
They ask simple questions, repeat stories, and depend on your patience the way you once depended on theirs. Very few understand this role reversal. What looks like innocence or inconvenience is really time coming full circle. Don’t correct them harshly. Don’t rush them. Care for them the way they once protected you. This is not a burden. It is repayment, quietly wrapped as love.

[MumZee✨🇳🇬 @_DebbieOA]

These videos are really educative.