Nigerian students Ayomide Obikoya and Kehinde Ajasa created the 'Natrifier,' a purification apparatus that removes oil pollutants from water. Their community has fought for clean water for over two decades.
Story by grantee @omololafolabi / @TheNationNews.https://t.co/jyzQC5LN7f
My girlfriend cried in my lap for two straight hours, literally two hours. Her mom has a drinking problem.
Seriously, no boy or girl should ever have to deal with a drinking problem in their family.
This was the first time that my cute panda cried, and I tried my best to comfort her. We spent a good time together afterward.
But one thought kept coming back again and again:
When will this stop?
Not if it will happen again, but when.
That is exactly what Geometric Distribution answers.
Geometric Distribution models the number of trials needed until the first success occurs.
In simple words: How many attempts are required before something succeeds for the first time?
Mathematical Definition
If the probability of success on each trial is p, then the probability that the first success happens on the k-th trial is:
Formula:
P(X = k) = (1 − p)^(k − 1) × p
Where:
- k = trial number of first success
- p = probability of success
- (1 − p) = probability of failure
Lets take an example and solve step by step
A person tries to have a calm, argument free evening at home. Each evening has a 20 percent chance of being peaceful.
What is the probability that the first peaceful evening occurs on the 5th day?
Step 1: Identify parameters
- k = 5
- p = 20% or 0.20
- (1 - p) = (1 - 0.20) = 0.80 or 80%
Step 2: Understand what "first success on the 5th day" means
For the first peaceful evening to happen on the 5th day:
- Day 1 must be a failure
- Day 2 must be a failure
- Day 3 must be a failure
- Day 4 must be a failure
- Day 5 must be a success
Step 3: Write the probability expression using multiplication
Because all days are independent, we multiply the probabilities.
- Probability that day 1 fails = 0.80
- Probability that day 2 fails = 0.80
- Probability that day 3 fails = 0.80
- Probability that day 4 fails = 0.80
- Probability that day 5 succeeds = 0.20
P = 0.80 × 0.80 × 0.80 × 0.80 × 0.20
P = (0.80^4) × 0.20
P = 0.0819 or 8.19%
Step 4: Verify with the formula
- P(X = k) = (1 − p)^(k − 1) × p
- P(X = 5) = (1 − 0.20)^(5 − 1) × 0.20
- P(X = 5) = (0.80^4) × 0.20
- P(X = 5) = 0.0819 or 8.19% ✅
Final Answer
There is an 8.19% chance that the first peaceful evening occurs on the 5th day.
Congratulations 🎉, you've just learned the Geometric Distribution.
Bonus: Applications in AI and ML
1. System reliability
How many attempts occur before a system completes a task successfully?
2. Network communication
How many retries are needed before a packet is delivered?
3. Reinforcement learning
How many episodes occur before the first reward is observed?
4. Fraud and anomaly detection
How many normal events occur before an abnormal one appears?
if you’re drawn to:
richard feynman
alan turing
claude shannon
john von neumann
nikola tesla
seymour papert
marvin minsky
judea pearl
dennis ritchie
donald knuth
rodd brooks
yann lecun
john carmack
dieter rams
elon musk
bjarne stroustrup
steve jobs
you’re not just into tech; you’re into the art of engineering,
the philosophy of systems, and the beauty of how things work.
you’ve found your people.
one minute, you're on the street of Ibadan searching for research labs to intern voluntarily without any positive response, the next minute, you're in europe getting properly welcomed into a top professor's research lab.🥳
Success is closely related to following your passion, but passion comes from the Latin word Passio, which means “to suffer.” So passion is not doing what you love; it’s finding something you are willing to suffer for. And suffering can only be bearable when you are resilient.
This resilience is what makes ordinary people achieve extraordinary results, and the beauty of it is that resilience in one field is replicable in another.
I have come to the realization that the major thing a first-class degree gives us is a chance to experience our own greatness — a chance to discover that you are resilient enough to acquire knowledge.
I STOPPED doing my best, I started doing what was required.
Let’s face it, sometimes your best is not enough, and that’s okay, but to avoid explaining how you failed, just do what’s required. Failure is Hard to Explain.
For me, tech, computer science and programming is just the means to an end and not the end itself. I want more out of life, do more with life, and then help shape someone’s else life. I have no idea on how to do these now, but I am pretty much sure Technology will help❤️
Mediocrity is the combination of Awareness and Acceptance. Being aware of not being good enough and Accepting it that way. If you are aware and you don’t want to accept, Congratulations, Keep Working!❤️