STAT midterms

• Random Sampling


  A sample selected from the population by a process that ensures that: The rules of probability apply to the sample, The sample is representative of the population
• Ways of Random Sampling


  • Randomly generated numbers to choose a sample
  • Dividing a population into groups with similar attributes
  • Dividing a population into groups, or clusters
• Types of Random Sampling

  • Simple Random Sampling
  • Stratified Random Sampling
  • Cluster Random Sampling
  • Systematic Random Sampling
• Systematic Random Sampling


  Sample every k'th element
• Sampling with Replacement


  Method of sampling in which each member of the population selected for the sample is returned to the population before the next member is selected
• Sampling without Replacement


  Method of sampling in which the members of the sample are not returned to the population before subsequent members are selected
• Probability


  The likelihood of a particular event of interest occurring
• Viewpoints of Probability


  • A Priori (Theoretical/Classical)
  • A Posteriori (Empirical)
• Probability is usually represented as a fraction or as a decimal and ranges from 0.00 to 1.00 (proportion)
• Addition Rule


  p(A or B) = p(A) + p(B) - p(A and B) for events that are not mutually exclusive, p(A or B) = p(A) + p(B) for events that are mutually exclusive
• Multiplication Rule


  p(A and B) = p(A)p(B) for independent events, p(A and B) = p(A)p(B|A) for dependent events
• Mutually Exclusive Events


  Both cannot occur together or if the occurrence of one precludes the occurrence of the other
• Mutually Exclusive Events


  • The probability of randomly picking a 10 or a 4 in one draw from a deck of ordinary playing cards
• Mutually Exclusive Events


  • The probability of rolling a 1 and an even number in a fair dice
• Not Mutually Exclusive Events


  The probability of occurrence of A plus the probability of occurrence of B minus the probability of occurrence of both A and B
• Not Mutually Exclusive Events


  • The probability of getting an ace or a club in one draw on a deck of cards
• With Replacement


  • The probability of getting an ace on two consecutive draws if you were to place the card back into the deck
• Independent Events


  • The probability of rolling "snake eyes" (one on die 1 and one on die 2) in a pair of fair dice
• Independent Events


  • The probability of rolling both odd numbers in a pair of fair dice
• The probability of rolling both odd numbers in a pair of fair dice is 3/6*3/6 = 9/36 or 0.25
• Independent Events


  • The probability of selecting a color blind male participant if you were to select 15 from a total population of 300 males (sampling with replacement)
• Color Blindness happens every 1 in 12 males
• Multiplication Rule without Replacement

  p(A and B) = p(A)p(B|A), the probability of occurrence of A times the probability of occurrence of B given A has occurred
• Without Replacement


  • The probability of getting an ace on two consecutive draws (sample without replacement)
• Independent Events


  • The probability of hitting the jackpot in the 6-58 lottery