stats and advance algebra

• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• Information, visit the Academic-Clinic website. Tell your friends and classmates to come find and join us. The more, the merrier. Good luck!
• Deciles


  • D1
  • D2
  • D3
  • D4
  • D5
  • D6
  • D7
  • D8
  • D9
• Deciles


  Nine score points required to divide a distribution into ten equal parts
• Percentiles


  Ninety-nine score points which divide a distribution into one hundred equal parts
• Percentile rank


  Percentage of cases below a given percentile
• Sequence function


  Function with consecutive integers as domain
• Infinite sequence


  Sequence function with domain as all positive integers
• Finite sequence


  Sequence function with domain as a finite set of positive integers
• Fundamental principle of counting

  Total number of ways to do k things independently is n1 * n2 * n3 * ... * nk
• Coin flips


  • 8 ways
  • 2 ways per coin
• Dice rolls


  • 36 ways
  • 6 ways per die
• an = a1rn-1


  1. a1

  2. r

  3. n-1
• 2/1 = 2
• 1/8 = 1/2
• 1/4 = 1/3
• The common ratio is 2
• Sn


  Sum of the first n terms of a geometric sequence
• Fundamental Principle of Counting

  For a group of k things, the first can be done independently in n1 different ways, the second can be done independently in n2 different ways, the third can be done independently in n3 different ways, and so on, until the kth thing, then the total number of ways in which the k things can be done in the stated order is n1 * n2 * n3 * ... * nk
• Coin flips


  • 3 coins can fall in 8 ways
• Dice rolls


  • 2 dice can fall in 36 ways
• Given the digits 0, 2, 5, 6, 9, there are 48 3-digit numbers that can be formed from these digits if no two digits are to be the same
• Of the 48 numbers formed, 30 are even, 18 are odd, and 24 are greater than 600
• If a digit may be repeated, 100 3-digit numbers can be formed from the given digits
• Permutation


  An arrangement of n different objects
• Permutations


  • 4 boys and 3 girls can be seated in a row of 7 chairs in 2,520 ways

  3 out of 10 students can be ranked 1st, 2nd and 3rd in 720 ways

  The word STATISTICS has 50,400 distinct permutations
• Circular Permutations


  Permutations obtained by arranging objects in a circular fashion
• Circular Permutations


  • 8 people can be seated at a round table in 5,040 ways
• Combinations


  Selections of r objects from n objects without regard to order
• Combinations


  • A committee of 4 can be chosen from a group of 8 people in 70 ways

  2 spades and 3 diamonds can be selected from a deck of 52 cards in 22,308 ways
• Probability


  The likelihood or chance of occurrence of an event
• Types of Probability


  • Subjective or Personalistic
  • Relative Frequency or Empirical
  • Classical or A Priori
• Subjective Probability


  A personal assessment of the likelihood of occurrence of an event, based on all evidence available