Statistics

• This is the list of all possible outcomes

  Sample Space
• Each outcome is called

  sample point
• Total number of sample point is called ?

  Cardinality
• NUmerical measure of a likelihood of the occurrence of an event

  Probability
• What is the properties of an event occuring

  0<=P(E)<=1
• If an event cannot occur it is

  P(E)=0
• If the event occurs anytime it is

  P(E)=1
• WHa do you call the event that occurs when event a does not occur?

  Complimentary probability
• This is rule is based on the fact that the probability of an event and the probability of that event's complement must be rqual to 1

  Complement Rule
• P'(A)=1-P(A)


  Complement rule
• What are the two ways of assigning the probability of an event?

  Classical probability and Empirical Probability
• This type of probability is used to determine the probability associated with games of chance.

  Classical approach
• In this probability there are two assumptions(1) outcomes must be mutually exclusive (2) The outcomes are equally likely to occur

  Classical approach
• What is the formula for getting the probability of an event?


  P(E)=n(E)/n(S) where n(E) is the number of occurence of event in sample space; n(s) is the cardinality of sample space
• In the sequence of events, the total possible number of ways all events can be performed is the product of the possible number of each individual can be performed

  Fundamental counting Principle
• Arrangement of object without repetition and order is important 


  Permutation
• Permutation formula where order is important

  nPr=P(n,r)=n!/(n-r)1 where n is the total number of objects and r is the size of permutation
• Arrangement of objects where order is not important

  combination
• Combination formula


  nCr=n!/(n-r)!r!
• method of finding probability that is based on cumulated historical data found through observations and not from theories

  Empirical approach
• Empirical Approach Formula 


  P(E)=n(E)/N where n(E) is the number of times the event has occured and N number of oppurtunities for an evet to occur
• is a function that associates a real number with each sample point

  Random variable
• it is a rule that assigns probabilities to the random variables

  Probability mass function
• is another way of presenting probability distribution

  Histogram
• What are the two general classifications of probability distribution according to the nature of variables involved

  discrete and continuous
• defines probabilities that are associated with dicrete random variables

  Discrete probability
• Normal distribution is and example of what type of probability distribution

  Continuous Probability Distribution
• is a graphical representation of probability distribution

  histogram
• Is a rule that assigns probabilities to the values of the random variables

  Probability Mass function
• what denotes proability of failure in a single trial?

  q
• This rule states that the probability of a variable X that is greater than or equal to the given value x is equal to 1 minus the probability of less than or equal to a given value x minus 1

  Complementary rule
• Complementary rule formula


  P(X>=x)=1=P(X<=[x-1])
• Two balls are drawn in succession with replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls.
• Four coins are tossed. Let P be the random variable representing the number of heads that occur.
• The sum of the probabilities in a probability distribution should always equal to one.
• Histogram


  • Plots the values of the random variable along the horizontal axis and the probabilities along the vertical axis.
• Random variable Y


  • 0
  • 1
  • 2
  • 3
• Possible outcomes when 3 coins are tossed

  • HHH
  • HHT
  • HTH
  • HTT
  • THH
  • THT
  • TTH
  • TTT
• The probability of each value of the random variable must be between or equal to 0 and 1.
• The sum of the probabilities of all values of the random variable must be equal to 1.