Flashcards
Chapter 6: Probability
Cards in this deck (20)
- 1Probabilitythe proportion of times that a certain event is expected to occur
the study of randomness and uncertainty - 2Sample space Sthe set of all possible outcomes of an experiment
- 3Eventa subset of S or a collection of outcomes of an experiment
each outcome is a simple event - 4Probability Rule AAny probability is a number between 0 and 1
- 5Probability Rule BAll possible outcomes together must have probability
- 6Probability Rule CThe probability that an event does not occur is 1 minus the probability that the event does occur
P(A') = 1 - P(A) - 7Mutually ExclusiveIf two events have no outcomes in common, that is they both cannot happen simultaneously,
- 8Mutually Exclusive EventsThe probability that one or the other of the two mutually exclusive events occur is the sum of their individual probabilities
P(A or B) = P(A) + P(B) - 9Independent EventsIf two events do not influence each other and if the knowledge about one does not help in the knowledge of the probability of the other, the events are said to be independent of each other
- 10Independent Event ProbabilityIf two events are independent, then the probability that they both happen is found by multiplying their individual probabilities
P(A and B) = P(A) * P(B) - 11Discrete variableIf and only if it takes on a finite number of values or a countably infinite number of values
- ex. number of students in a class - 12Continuous variablewhen it takes on values which lie on a continuum or an interval of the real line
- ex. amount of water in a gallon bucket - 13Probability distribution of Discrete Random variableexpressed by a probability mass function (pmf) and a probability histogram
- 14ParameterWhen p(x) = P( X = x ) depends on a quantity which can take on various values
- 15Rule for PMFIf you have a probability model for a discrete random variable X...
1. each probability must be a number between 0 and 1
2. probabilities must add up to 1
- 16Expected Value of Discrete Random variablesDef: The long term average value of a random variable.
The expectation or mean of X is given by
- 17Variance and Standard Deviation of Discrete random variables
- 18Probability Density Function (pdf)the mathematical model for a continuous random variable X
- 19Probability Density Curvethe graph of the probability density function (pdf)
the curve that smoothes out a histogram
- 20Properties of a Property Density Function (pdf)For any value of a random variable X for which X is defined, f(X) should be non-negative
The total area under the probability density curve should be 1