Probability rules, conditional probability, binomial and geometric distributions, expected value and sampling distributions.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the addition rule of probability?
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P(A or B) = P(A) + P(B) - P(A and B)- When are two events mutually exclusive?
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When they cannot occur at the same time; P(A and B) = 0- What is the multiplication rule for independent events?
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P(A and B) = P(A) × P(B)- What does the complement rule state?
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P(not A) = 1 - P(A)- Define conditional probability P(A|B).
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The probability of event A occurring given that event B has already occurred- What is the formula for conditional probability?
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P(A|B) = P(A and B) / P(B)- When are two events independent?
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When the occurrence of one does not affect the probability of the other; P(A|B) = P(A)- What is Bayes' theorem used for?
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Finding the probability of a cause given an observed effect, or updating probability based on new information- List the four requirements for a binomial setting.
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Fixed number of trials, two outcomes per trial, constant probability of success, independent trials- What is the formula for binomial probability?
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P(X = k) = C(n,k) × p^k × (1-p)^(n-k)- What is the mean of a binomial distribution?
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μ = n × p- What is the standard deviation of a binomial distribution?
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σ = sqrt(n × p × (1-p))- What does a geometric distribution model?
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The number of trials needed to get the first success- What are the requirements for a geometric setting?
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Two outcomes per trial, constant probability of success, independent trials, counting trials until first success- What is the formula for geometric probability?
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P(X = k) = (1-p)^(k-1) × p
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