Discrete Probability Flashcards
Discrete probability
A discrete probability can only take certain values.
Discrete random variable
represents a possible numerical value from an
uncertain event. Can only assume a countable number of values. Examples: Roll
a dice twice. Let X be the number of times 4 comes up, thus X could be 0, 1, or 2
times. Toss a coin 5 times. Let X be the number of heads, thus X could = 0, 1, 2,
3, 4, or 5.
Covariance
The covariance measures the direction of a linear relationship between two variables. (Association)
4 essential properties of the binomial distribution
A fixed number of observations
Two mutually exclusive and collectively exhaustive events
Constant probability for each observation
Observations are independent
Fixed number of observations
A fixed number of observations, or trials, n.
E.g. 15 tosses of a coin; ten light bulbs taken from a warehouse.
Two mutually exclusive and collectively exhaustive events
Two mutually exclusive and collectively exhaustive categories. E.g. head or tail in each toss of a coin; defective or not defective light bulb. Generally called ‘success’ and ‘failure’. Probability of success is p, probability of failure is 1–p.
Constant probability for each observation
Constant probability for each observation. E.g. Probability of getting a tail is the same each time we toss the coin.
Observations are independent
Observations are independent. The outcome of one observation does not affect the outcome of the other. Two sampling methods can be used to ensure independence; either: Selected from infinite population without replacement or selected from finite population with replacement.
4 possible binomial scenarios
A manufacturing plant labels items as either defective or acceptable.
A firm bidding for contracts will either get a contract or not.
A market research firm receives survey responses of ‘yes I will buy’ or ‘no I will not’.
New job applicants either accept the offer or reject it.
Index numbers
Index numbers allow relative comparisons over time. Index
numbers are reported relative to a Base Period Index. Base period index = 100 by
definition. Used for an individual item or measurement.
Aggregate price index
An aggregate index is used to measure the rate of change from a base period for a group of items.
Which price index to use
Paasche is more accurate but more difficult to achieve.
2 types of random variables
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Discrete probability distribution toss 2 coins example
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Expected value
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Variance and standard deviation of discrete random variables
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Covariance formulas
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Computing the mean example
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Computing the standard example
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Computing the covariance example
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Interpreting mean, standard deviation and covariance
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The sum of two random variables
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Portfolio expected return and expected risk
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Portfolio example
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