Alright, future engineers!
**Expected Value (E[X]):** The average outcome you'd expect if an event is repeated many times.
Ex: Rolling a fair 6-sided die, E[X] = 3.5.
Pro-Tip: Essential for evaluating risk & long-term profitability in engineering decisions!
I have a fun math coincidence on my family: every year the birthday for both my parents and I is on the same weekday. All of them is past February, so this is always true.
What's the probability of this happening?
Is it as simple as P(x) = 1/7*1/7*1/7 or do we take anything in consideration to properly calculate the probability? #math #mathhelp #fedihelp #probability #hivemind
There is a non-zero #probability that we are a collective of Boltzmann brains...
...and if the universe is truly infinite...
That probability is 1...
Hello my fellow Boltzmann brains!
Alright, future engineers!
Events are **Mutually Exclusive** if they can't happen simultaneously. Ex: Rolling a 1 & 2 on one die (P(A & B) = 0). Pro-Tip: If events are ME, P(A or B) = P(A) + P(B). Crucial for simplifying many prob. calculations!
Alright, future engineers!
**Law of Large Numbers:** As you run more trials, the observed average of random events gets closer to its true expected value. Ex: Flip a coin 1000 times, heads will be ~500. Pro-Tip: It's why casinos always win! More data gives a better estimate of true probability.
Alright, future engineers! **Conditional Probability P(A|B)** is P(A) given B already happened. Formula: `P(A|B) = P(A and B) / P(B)`. Pro-Tip: Use it to refine predictions with new info! Crucial for risk assessment & diagnostics.
RE: https://mathstodon.xyz/@kangmeister/116136852073418222
It was almost exactly two years ago in Lunteren after a pitch by Ton de Kok (director of CWI at the time) that the idea for this popped into mind. And now (after a lot of hard work!) it is in full swing. An exciting mix of people at the confluence of combinatorics, algorithms, probability, brought together in Amsterdam over the next couple of months!
Alright, future engineers!
Central Limit Theorem (CLT): Sample means tend towards a Normal Distribution as sample size grows, regardless of parent distribution. Ex: Avg weights from many small batches form a bell curve. Pro-Tip: Crucial for inference; it lets us use normal stats even with non-normal data!
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