Term
| What does a probability distribution describe? |
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Definition
| the probabilities of all the possible outcomes for a random variable. |
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Term
| Whats the formula for defining the conditional probability of A given B: |
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Definition
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Term
| What's the formula for calculating the probability that at least one of two events will occur? |
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Definition
| P(A or B) = P(A) + P(B) - P(AB) |
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Term
| When dealing with independent events the word and indicates... and the word or indicates... |
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Definition
and indicates multiplication
or indicates addition |
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Term
| What is a frequency distribution? |
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Definition
| a tabular presentation of statistical data that aids the analysis of large data sets. |
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Term
| What are the steps involved in constructing a frequency distribution? |
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Definition
- Define the intervals (intervals must be mutually exclusive, an observation can be placed in only one interval)
- Tally the observations
- Count the observations
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Term
| How do you calculate relative frequency? |
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Definition
| = frequency of each return inverval / total number of observations |
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Term
| What's Bayes's formula used for? |
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Definition
| used for updating a given set of prior probabilities for a given event in response to the arrival of new information. |
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Term
| Give the formula for Bayes theorem: |
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Definition
| updated probability = (probability of new information for a given even / unconditional probability of new information) * prior prability of event |
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Term
| What are the 2 key properties of a probability function: |
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Definition
- p(x) is between 0 and 1
- the sum of probabilities for all possible outcome = 1 |
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Term
| Whats the main difference between the pdf and a cdf? |
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Definition
- a probability density function can be used to generate the probability that outcomes of a continuous distribution lie within a particular range of outcomes.
- a cdf defines the probability that random variable X takes on a value equal to or less than a specific value. |
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Term
| What's a discrete uniform random variable? |
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Definition
| its one for which the probabilities for all possible outcomes for a discrete variable are equal |
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Term
| What are the key properties of the normal distribution? |
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Definition
- X is normally distributed with mean μ and variance σ2
- A linear combination of normally distributed random variables is also normally distributed
- The probabilities of outcomes further above and below the mean get smaller and smaller but do not go to 0 (the tails get very thing but extend infinitely)
- It's an example of a cdf where the total area under the curve = 1 |
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Term
| Whats a univariate distribution? |
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Definition
| the distribution of a single random variable |
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Term
| What's a multivariate distribution? |
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Definition
specifies the probabilities associated with a group of random variables and is meaningful only when the behaviour of each random variable in the group is in some way dependent upon the behaviour of the others.
Multivariate distributions between two discrete random variables are described using joint probability tables. |
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Term
| What marginal probability of an event? |
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Definition
it's the unconditional probability of that even.
i.e. with multivariate distributions, the marginal probability of x is the same of all probability values of x (i.e. not conditional on the value of y). |
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Term
| Whats the formula for defining the conditional probability function of Y given X? |
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Definition
| f(y given x) = f(x,y) / f(x) |
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