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Appendix: Discrete Algebra

    A combination is a selection of objects considered without regard to their order. For all positive integers n and r, where r £ n, the number of combinations of n things taken r at a time is _nC_r = _nP_r / rP_r = n! / (n – r)!r!

    After know the basic concepts above, you can start doing probability. The probability of an event is the ratio of the number of outcomes in the event to the number of outcomes in the sample space. If A and B include all outcomes of S, and A and B have no outcomes in common, Event A is the complement of event B with respect to sample space S. The complement of A is denoted A. Here are some additional properties of probability:

    Two events A and B are mutually exclusive if and only if they have no outcomes in common. Two events A and B are independent if and only if

  P(A and then B) = P(A) x P(B).

  For any two events A and B in sample space S,

  P(A or B) = P(A) + P(B) x P(A and B).

For all positive integers n,

  (a + b)ⁿ = C_naⁿ + _nC_n-1a^n-1b + _nC_n-2a^n-2b² +…+ _nC₁ab^n-1 + _nC₀bⁿ

Statistics   

    Data is everywhere in people’s lives. And this is where we need the statistics. Statistics is a large area of math, and we can’t cover much here. So we are just going to talk about some basic concepts. First you have to know data. Data is a collection of information. A set of data can be described by its center, or central tendency, and its dispersion. There are five most important concepts about data or statistics. They are mode, median, lower quartile, range, and mean.

  The mode is a set of data is the number or numbers that occur with greatest frequency.

  The median is a measure of central tendency. It is the middle number of an ordered set of numbers. If a set has an even number of members, the median is midway between the two middle numbers.

  The lower quartile is the median of the numbers below the median of a set of data. The upper quartile is the median of the numbers above the median. The median and quartiles divided the set into approximately equal quarters.

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