#probstats — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #probstats, aggregated by home.social.
-
Alright, future engineers!
**Bayes' Theorem:** Updates an event's probability (hypothesis) based on new evidence.
Ex: P(H|E) = [P(E|H) * P(H)] / P(E).
Pro-Tip: Essential for diagnostic tests & updating beliefs with new data! Use it to refine predictions.
#ProbStats #Bayesian #STEM #StudyNotes -
**Conditional Probability:** The likelihood of an event occurring *given* another event has already occurred.
Ex: P(A|B) = P(A and B) / P(B).
Pro-Tip: The given event B *defines* your new, reduced sample space. Focus only on outcomes where B happened!
#ProbStats #DecisionMaking #STEM #StudyNotes -
Alright, future engineers!
**Expected Value (E[X]):** The long-run average outcome of a random variable.
Ex: For discrete X, `E[X] = Sum(x * P(x))`. Avg winnings in a game!
Pro-Tip: Key for decision-making in uncertainty & risk assessment.
#ProbStats #RiskAnalysis #STEM #StudyNotes -
Alright, future engineers!
**Combinations:** Choosing items where order *doesn't* matter.
Ex: Selecting 3 friends from 5 for a team. C(5,3) = 10 ways.
Pro-Tip: Think groups or sets. Changing the order doesn't create a new combination!
#Combinatorics #ProbStats #STEM #StudyNotes -
Alright, future engineers!
**Permutations:** Selecting items from a set where *order matters*.
Ex: Arranging 3 items (ABC, ACB...). P(n,k) = n!/(n-k)!
Pro-Tip: Think specific sequences or rankings. Order defines a *new* permutation!
#ProbStats #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
**Normal Distribution:** A common bell-shaped probability distribution where most data clusters around the mean.
Ex: Heights or test scores often follow this curve. `X ~ N(mu, sigma^2)`
Pro-Tip: The 68-95-99.7 Rule is your shortcut for understanding data spread! -
Alright, future engineers!
**Normal Distribution:** A common bell-shaped probability distribution where most data clusters around the mean.
Ex: Heights or test scores often follow this curve. `X ~ N(mu, sigma^2)`
Pro-Tip: The 68-95-99.7 Rule is your shortcut for understanding data spread! -
Alright, future engineers!
**Permutations:** The number of ways to arrange a set of items where *order matters*.
Ex: Arranging 3 books (A,B,C) two at a time: AB, BA, AC, CA, BC, CB. (6 ways). `P(n,k) = n!/(n-k)!`
Pro-Tip: Order matters! is your key phrase to spot them!
#Combinatorics #ProbStats #STEM #StudyNotes -
Alright, future engineers!
**Permutation:** An *ordered* arrangement of 'k' items chosen from 'n' distinct items.
Ex: Arranging 3 books from 5: `5P3 = 5!/(5-3)! = 60` ways.
Pro-Tip: The *order* or sequence is crucial! Think distinct positions or roles.
#ProbStats #Counting #STEM #StudyNotes -
Alright, future engineers!
**Combination:** An *unordered* selection of 'k' items from 'n' distinct items.
Ex: Choosing 3 people from 5: `5C3 = 5!/(3!2!) = 10` ways.
Pro-Tip: Order DOES NOT matter! If order matters, use Permutations.
#ProbStats #Counting #STEM #StudyNotes