ProbStats Flashcard 4A Review - Discrete Probability Distributions

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What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of outcomes for a discrete random variable, which can take on a countable number of values.

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What is the expected value in probability?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability of occurrence.

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How do you calculate the expected value of a discrete random variable?

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To calculate the expected value (E[X]), multiply each possible value of the random variable (x) by its probability (P(x)) and sum the results: E[X] = Σ (x * P(x)).

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What does it mean to lose $88.89 in a game?

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It means that, on average, a player can expect to lose $88.89 for each game played, considering the probabilities of winning and losing.

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What is the probability of an event?

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The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 (impossible) and 1 (certain).

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How do you find the probability of multiple events occurring?

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To find the probability of multiple independent events occurring, multiply the probabilities of each individual event.

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What is the standard deviation in probability distributions?

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The standard deviation is a measure of the amount of variation or dispersion in a set of values, indicating how much the values deviate from the expected value.

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How do you calculate the standard deviation of a discrete random variable?

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To calculate the standard deviation, first find the expected value, then compute the variance by summing the squared differences between each value and the expected value, weighted by their probabilities. Finally, take the square root of the variance.

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What does 'at least 1' mean in probability?

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'At least 1' means that the event can occur one or more times, and its probability can be calculated as 1 minus the probability of the event not occurring at all.

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What is the complement rule in probability?

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The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring: P(A) = 1 - P(A').