Please enable JavaScript.

Coggle requires JavaScript to display documents.

Maths, Stats - Coggle Diagram

- - - - X~B(n, p)
      - X is what you are testing: e.g. winning a game, the height of a flower stem
  - - - P(Win) = 1/6
        Number of trials = 20
      - X~B(20,1/6)
        
        Where X = 'number of sixes'
        
        P(X=8) = 20C8 (1/6)^8(5/6)^12
        
        8.41*10^(-3)
        
        Number of wins * number of losses * number of ways this can happen
        
        Calculator : Distribution (Option 7), Binomial PD (Option 4), Variable (Option 2)
        
        x=8, N=20, p=1/6
        
        8.41*10^(-3)
  - - - If relevant, state any assumptions to go with this
        
        State probability you're trying to find
        
        e.g. P(x=6), P(x>11)
        
        Use Binomial PD function on calculator to find this probability if it's a single value (=)
        Use Binomial CD if it's a range (>, <, =<, =>)
        
        Binomial CD works with "P(X≤x)", so if you have:
        
        P(X<x), convert it to P(X≤x+1)
        
        P(X>x), convert it to 1-P(X≤x)
        
        P(X≥x), convert it to 1-P(X≤x-1)
        
        Use diagrams to help with this because it's easy to mess up!
        
        Use this result (the probability) to answer the question, usually converting it to 3 significant figures unless stated otherwise
        
        Remember to write this in the context of the question
        
        (e.g. fixed probability of rolling a 6, not just fixed probability!)
- - - - This means the mean is the most likely option, and values further away from the mean are increasingly less likely
    - - Most calculators have functions to find approximate probabilities
  - - - E.g. height, time
  - - - These give a good estimate
      - If asked to prove this ["Prove that points of inflection occur at x = ±σ"],
        find the 2nd derivative of the curve, let it = 0
        Factorise so that you can have 2 or more brackets equal to 0 to complete the equation
        Rule out that one of the brackets can't = 0, therefore the other one must
        Make a new equation where this bracket = 0
        Solve to get x=±σ
  - - - X~N(μ,σ²)
  - - - z = (x-μ)/σ