Data Management

Data Management

1. Permutations

   • Fundamental Counting Principle
     • Tree Diagrams
     • If one activity can occur in "m" ways, and second activity can occur in "n" ways, then both activities can occur m*n ways
   • Rule of sum
     • "a" ways of doing things + "b" ways of doing things gives you "a+b" ways to chose one of the actions
   • nPr = n! / (n − r)!
     • Ordered arrangement of objects
   • Identical Items
     • n!/a!b!c!…
       • When permutation of "n" objects has "a" identical items, "b" identical items, etc.
   • Factorial Notation
     • Used when a number is multiplied by every whole # between 1 and itself
   • Order Matters

2. Probability

   • Type of Probabilities
     • Subjective Probability
       • Estimate of the likelihood based on intuition and experience
     • Experimental Probability
       • Based on direct observation
         • determined by dividing the number of times the favorable outcome occurs by the total number of trials
     • Theoretical Probability
       • Probability of event a deduced from analysis of possible outcomes
   • Complement of Event "A"
     • P(A') + P(A) = 1 P(A') = 1-P(A)

3. Combinations

   • nCr = n!/(n-r)!r!
   • Order Does Not Matter
     • How many ways can 5 cards be selected from a deck of 52 cards if the order in which they are chosen does not matter?
   • Fundamental Counting Principle
     • Ursula runs a small landscaping business. She has on hand 12 kinds of rose bushes, 16 kinds of small shrubs, 11 kinds of evergreen seedlings, and 18 kinds of flowering lilies. In how many ways can Ursula fill an order if a customer wants a) 15 different varieties consisting of 4 roses, 3 shrubs, 2 evergreens, and 6 lilies?
   • Rule of Sum
     • b) either 4 different roses or 6 different lilies?
   • Pascal's Triangle
     • tn,r
       • n = row # r = place in row
         • tn,r = tn-1,r-1 + tn-1,r
         • nCr
     • Sum of the terms in row n of Pascal’s triangle
       • 2^n
   • Binomial Theorem
     • The coefficients of the terms in the expansion of (a + b)n correspond to the terms in row n of Pascal’s triangle.
       • (a + b)n = nC0an + nC1an−1b + nC2an−2b2 + …

4. Non-Mutually Exclusive Events

   • Events that can occur at the same time
     • P(AUB) = P(A) + P(B) - P(A and B)

5. Mutually Exclusive Events

   • Events that can not occur at the same time
     • P(AUB) = P(A) + P(B)

6. Probability

7. Venn Diagrams

   • Help visualize relationships between sets of items, especially when they have common elements
     • n(AUB) = n(A) + n(B) - n(A and B)

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