7.1 Discrete Probability Distributions SPRING 2023

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What is a probability distribution?

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A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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What are the two main types of probability distributions?

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Discrete and Continuous probability distributions.

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What is a discrete probability distribution?

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A discrete probability distribution is one that shows the probabilities of outcomes with finite values, such as the number of cars in a household.

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What is the sum of probabilities in a probability distribution?

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The sum of all probabilities in a probability distribution must equal 1.

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How do you calculate the probability of at least 'k' successes in a discrete distribution?

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To find the probability of at least 'k' successes, sum the probabilities of all outcomes from 'k' to the maximum possible value.

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What is a permutation?

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A permutation is an arrangement of objects in a specific order, where the order matters.

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What is a combination?

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A combination is a selection of objects where the order does not matter.

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In a probability distribution table, what does P(X) represent?

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P(X) represents the probability of the random variable X taking a specific value.

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What is the probability of getting exactly 'k' successes in a binomial distribution?

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The probability is calculated using the formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials and p is the probability of success.

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What is the expected value in a probability distribution?

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The expected value is the long-term average or mean of a random variable, calculated as E(X) = Σ [x * P(X=x)].

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