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Discrete random variable-
A discrete random variable is a random variable that can take on only a finite or at most a countably infinite number of values
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Basic description of the probability mass function:
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cumulative distribution function (cdf)
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Random variable
a numeric outcome from a random problem
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support-
The values a random variable can take on is the support of a variable
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The probability of k successes in a binomial distribution:
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Probability of all the variation of successful sequences in a binomial distribution
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Use of capital and lower case letters to describe random variables and their realizations
- capital= random variable possibilities
- lowercase= realization (set of finite/interval of values)
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Continuous random variables
has an interval or union of intervals as its support
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distribution-
pattern and frequency we observe the random variable
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Formula for a geometric distribution
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Formula for a negative binomial distribution
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What do you get when you take the integral of a PDF?
probability!
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Endpoints don't matter if you are finding probabilities for continuous functions
T/F
True
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How do you find probability from a PMF?
- sum of the range it has support for
- (discrete)
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How do you find probability for a PDF?
Integrate over the range of interest
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Endpoints don't matter for a PMF
T/F
False
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What are values of the PDF often refered to as?
relative liklihoods
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In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: population
all coins of this type
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In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: parameter
=p= P(coin lands on heads)
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In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: sample
Sequence of observed coin flips
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In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: Statistic
observed number of heads (y) or sample proportion of heads
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Support-
values the random variables can take on
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The differences between CAPITAL and lowercase variables
ex. X vs x
little 'x' represents realization of the random variable
big 'X' represents the actual random variable
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Support for a discrete random variable
countable support
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Support for a continuous random variable
interval (or union of intervals) for the support
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How can you identify a CDF of a random variable Y?
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Cumulative Distribution Function (cdf) of a random variable (Y)
denoted as either: or
The cumulative probability up to and including the actualized value of (y)
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Frequency function
The probability mass function of a discrete random variable:
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Probability density function (PDF)
- a continuous random variable is the function that satisfies:
- or
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Describe a PDF
PDF is a visualization of the distribution of your random variable
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For discrete random variables, the probabilities are the sum of the PMF over the range of interest and (end points do matter)
T/F
True
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For continuous random variables, the probabilities are the integrals of the PDF over the range of interest and (end points do matter)
T/F
- False
- End points DO NOT matter
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Solving for probability for a discrete variable:
(PMF or PDF? describe how to solve)
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Solving for probability for a continuous variable:
(PMF or PDF? describe how to solve)
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integrating factor=
constant required to make an integral = 1
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What are the values of the PDF often refered to as?
"relative likelihoods"
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Does f(a) or f(b) have a higher liklihood?
f(a)
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Formula for finding probability from a CDF:
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Formula for finding probability from a PDF:
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Formula for finding probability from a PMF:
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Expected value for a random variable Y:
- Expected Value (or Mean) of a RV Y , denoted as E(Y)= µY , is the average value of Y weighted by the probability distribution.
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