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21 Cards in this Set
- Front
- Back
What are the two types of Discrete Probability Distributions?
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- Binomial
- Poisson |
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What are the two types of Continuous Probability Distributions?
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- Normal (Gaussian)
- Others (t, F, Chi-Square) |
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Binomial
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Discrete probability
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Which four characteristics define a Binomial distribution?
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- Fixed number of trials (n)
- Two possible outcomes; "success" or "failure" - P is constant; Probability of success (p) is the same for each trial - Trials are independent; outcome of one trial does not affect outcome of another trial |
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What is each Binomial trial known as?
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Bernoulli trial
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What is the random variable in a binomial distribution and what is it called?
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- total number of successes out of 'n' trials
- Called the binomial random variable |
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What is the Binomial Probability Distribution?
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- List of probabilities
- Lists the probabilities that a success will occur x times in 'n' trials for each possible value of x |
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What are the ways of obtaining values from the binomial distribution?
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- Tables
- Binomial Formula - Calculator - Excel - Internet calculator - Normal approximation when n is large |
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Using table to find Binomial Distribution
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- Find table with right number of trials (n)
- Find column with same probability (p) |
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When is a binomial distribution symmetric?
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when p = 0.5
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What does it mean in a binomial distribution when p = 0.5?
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The binomial distribution is symmetric
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Mean (Binomial)
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E (X) = np
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Variance (Binomial)
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V (X) = npq
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Standard Deviation (Binomial)
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SD = square root of npq
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What is q?
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1 - p; probability of failure
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Poisson
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Discrete Probability
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Which four characteristics define a Poisson distribution?
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- Trials are independent (number of successes that occur in an interval is independent of number of successes in any other interval) and random
- P is constant; probability of success is the same for all equal size intervals - Probability of success in an interval is proportional to the size of the interval - Probability of more than one success in an interval approaches zero as the interval size approaches zero |
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Poisson random variable
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- Measures the number of success in an interval (time, length, area)
- Number of occurrences of a relatively rare event that occurs randomly and independently |
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What must you remember about the given average and the time interval?
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Adjust the given average for the time interval if needed
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Binomial Summary
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Gives us the probability that a success will occur x times in 'n' trials
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Poisson Summary
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Number of occurrences of a relatively rare event that occurs randomly and independently
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