S2 - Chapter 1 to 5

Binomial Distribution
1. Conditions of trials
  1. Fixed amount
  2. Success or failure
  3. Independent
  4. Probability of success is constant
2. P(X=x) = P(X≤x) - P(X≤(x-1))
Poisson Distribution
1. Conditions of events
  1. Occur singly in space or time
  2. Occur at a constant rate
  3. Independent
  4. Random
2. If X~B(n,p) and n is large + p is small
  1. X can be approximated by Po(np)
Continuous Random Variables
1. Area under graph = 1
2. f(x) = Differential of F(x)
3. F(x) = Integral of f(x)
4. Median - F(m) = 0.5
  1. Lower Quartile - F(Q1) = 0.25
    1. Upper Quartile - F(Q3) = 0.75
5. Mode is the highest point of the function
Continuous Uniform Distribution
Normal Approximations
1. Approximating binomial by a normal distribution
2. Approximating a poisson distribution by a normal distribution
Populations and samples
1. Census
  1. Information obtained from every individual
  2. Every member is used
  3. Unbiased
  4. Gives an accurate answer
  5. Time consuming
  6. Costly
  7. Hard to ensure the whole population is surveyed
2. Sample
  1. If population is too big, samples are used
  2. Investigation using a sample is called sample survey
  3. Individual units are called sampling units
  4. Can be representative of population if it is large and well mixed

Zusammenfassung der Ressource

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