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39 Cards in this Set
- Front
- Back
Variable
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symbol for unspecified quantity: a symbol that represents an unspecified or unknown quantity
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Constants
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quantity with fixed value: a mathematical quantity that retains a fixed value in any circumstances or throughout a particular set of calculations
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Functions
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a function takes one or more input variables and uses some predetermined formula to give us an output value
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Experiment
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is a process, natural or controlled, that generates well-defined outcomes which can be observed or measured
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Simple Event
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a most basic outcome that is observed on a single realization of an experiment
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Event
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a collection of simple events
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Sample Space
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one single big events that contains all possible simple events (from the same process) of an experiment
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Mutually Exclusive
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two or more events if when any single one of them occurs, the others cannot occur
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Priori Probability
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probability is based on our prior, or existing, knowledge of the process by which the event of interest occurs
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Empirical Probability
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probability involves surveys that generate data from which can calculate the probability; we have no, or insufficient, prior knowledge of the event-generating process itself, so we rely on data
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Subjective Probability
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probability is probability as perceived by each individual (or organization). It's based on the decision maker's personal experience, opinion, or interpretation of a particular situation.
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Joint Probability
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refers to the probability of two or more events, i.e., the probability of a union of events
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Frequency
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number of occurrences of statistical result: the number of times a particular result occurs in a statistical survey (absolute frequency), or the ratio of that number to the total results obtained in the survey (relative frequency)
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Relative Frequency Formula
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Histogram
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is a special column chart where the numerical data is grouped into brackets and the frequency of each bracket is represented by the height of a vertical column
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Contingency Table
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is a statistical tool (not specific to Excel!) that presents the joint frequencies of two categorical variables as cross tabulations
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Joint Probability
P(AB) or P(A∩B) |
is the probability of two events occurring together (either at the same time, or one after other but considered together as one single event with two stages). It's the probability of the intersection of two events: the likelihood of both events happening
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Conditional Probability
P(A|B) |
when two events A and B are considered together, we often want to know what the probability of one event is given that the other event also happens.
P(A|B), read as "the probability of A, given B". We assume B represents the event that occurs "first", and A the second event. |
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Statistical Independence
P(A|B) = P(A) and P(B|A) = P(B) |
Two event A and B are said to be (statically) independent of each other if the occurrence of A does not affect the probability of B, and vice versa.
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Random Variable
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is a mapping defined for a given experiment and the experiment's associated sample space. Each value of the random variable must be a real number and represents a (simple) event in the sample space.
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Quantitative Events
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If an event is already numerical in nature, the random variable is simply defined to take on values of the events themselves.
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Qualitative Event
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Event is not numerical in nature. (e.g., gender, state of birth, a person's name, a security's CUSIP. a course number at UH such as ECON 2370)
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Discrete Random Variables
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map simple events to a countable (or discrete) set of real numbers, such as a finite set of whole numbers. One way to recognize a discrete RV (random variable) is to check whether the number of permissible values for the RV is finite.
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Continuous Random Variables
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map simple events to an interval of real numbers; as we know from basic algebra, an interval of real numbers is not countable.
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Probability Distributions
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mathematical functions that associate the values of the random variables with probabilities.
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pmf (probability mass function)
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the probability function of a discrete random variable is a function that maps each value of the discrete random variable to a probability.
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cdf (cumulative distribution function)
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cdf of discrete RV X is defined as, Fx (x) = P (X ≤ x)
The weak inequality inside the parenthesis on the right-hand side represent all the simple events whose mapped values are less than or equal to x. |
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Weighted Average Formula
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Mean
(expected value or expectation of a random variable) |
is the weighted average of all the values of he RV, where the weights are the point probability measures
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Variance Deviation
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is the weighted average of the squared deviation of RV values from the mean, where the weights are once again the point probability measures, or, in the case of discrete RVs, the pmf values
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Variance Deviation function
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Standard Deviation
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is defined as the square root of the variance
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Standard Deviation function
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Descriptive Statistics
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This is when we calculate statistical properties, such as mean, median, standard deviation, correlation, on data we have collected. We use descriptive statistics to describe the data in statistical terms
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Inferential Statistics
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This is when we try to draw conclusions about the source of the data, given the descriptive statistics we have calculated. We use inferential statistics to understand and to model the statistical properties of the data source and, in some cases, to make forecasts.
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Population
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the entire group of individuals or items from which a sample may be selected for statistical measurement
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Sample
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a representative selection, meaning the sample should reflect the general characteristics of the population.
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A⊥B
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independent (e.g., getting an odd and even number at the same time)
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A∩B ≠ 0
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Mutually Exclusive
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