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34 Cards in this Set
- Front
- Back
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What is Rare Event Rule for Inferential Statistics?
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If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
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What is an event?
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any collection of results or outcomes of a procedure.
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What is a simple event?
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is an outcome or an event that cannot be further broken down into simpler components.
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What is the sample space?
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a procedure consists of all possible simple events. That is the, the sample space consists of all outcomes that cannot be broken down any further.
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What does P denote?
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Probability
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What does A, B, and C denote?
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Specific events. Even A , event B etc.
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Explain P(A)?
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denotes the probability of event A occuring.
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What is the formula for Relative Frequency Approximation of Probabili`ty?
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Number of times A occurred
P(A) = ------------------------------------------ Number of times the procedure was repeated. |
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What is the classical approach to Probability (requires equally likely outcomes) formula?
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Number of ways A can occur
P(A) = ---------------------------------------- Number of different simple events |
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What is the classical approach to Probability (requires equally likely outcomes) formula in simple terms?
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s
P(A) = ___ n |
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What is subjective probabilities?
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P(A) , the probability of even A, is estimated by using knowledge of the relevant circumstance.
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What are the 3 approaches to finding a probabilty?
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relative frequency approach, classical approach, & subjective probability.
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Explain the relative frequency approach and show examples?
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Using the relative frequency approach we obtain an approximation instead of an exact value. Use n to determine the # of observation in a large sample.
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Explain the classical approach and show examples?
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the approach has equally likely outcomes but n= total # of observations in the experiment. We will use this most often.
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Explain the subjective approach and show examples?
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in subjective the opinion counts. Like we take into account changes in safety rules, new technologies, etc to determine accidents in workplace
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How do express probabilities?
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Always express probabilities as a fraction or decimal number between 1 and 0. (Dr. Ibara like 0.0001 spaces)
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What number is the probability of an impossible event?
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zero = 0
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What number is the probability of an event that is certain to occur?
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One = 1
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What does it mean when- for any even A, the probability of A is between 0 and 1 inclusive?
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What is the symbol for the complement of even A?
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What does complement of an event mean?
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consists of all outcomes in that event does not occur.
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What is a compound event?
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any event combining two or more simple events.
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What is the addition rule formula?
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P(A or B)= P(in a single trial, event A occurs or Event B occurs of they both occur).
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What is the significance of "or" in probabilities?
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They can either mean A occurs or B occurs or A&B occurs
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What is the formula for the formal addition rule?
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P(A or B) = P(A) + P(B) - P(A & B)
where P (A & B) denotes the probability that A and B both occur at the same times as an outcome in a trial or procedure. |
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What is the intuitive addition rule?
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to find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is = to that sum, divided by the total # of outcomes in the sample space.
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When are events A & B disjointed or mutually exclusive?
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If they cannot occur at the same time
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What are the 3 rules of complementary events?
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What is the notation for conditional probability?
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P( B|A ) represents the probability of even B occurring after it is assumes that even A has already occurred. (we can read B|A as "B given A" or as "event B occurring after even A has already occured.")
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What is the term when the occurrence of even A does not affect the probability of the occurrence of the other?
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Events A and B are independent of each other.
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If A and B are not independent, they are said to be what?
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dependant
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What is the formal multiplication rule?
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P(A and B) = P(A) X P( B|A )
If A and B are independent events, P( B|A ) is the same as P(B) |
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What is the intuitive multiplication rule?
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When finding the probability that event A occurs in one trial and event B occurs in the next trial, multiply the probability of even A by the probability of even B , but be sure that the probability of even B takes into account the previous occurrence of even A.
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What is treating dependent events as independent: the 5% guideline for cumbersome calculations?
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If calculations are very cumbersome and if a sample size is no more than 5% of the size of the population , treat the selection as being independent (even if the selections are made without replacement, so they are technically dependent).
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