Discrete Probability Distributions

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What is a discrete probability distribution?

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A discrete probability distribution is a statistical distribution that describes the likelihood of each possible outcome of a discrete random variable.

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What is a random variable?

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A random variable is a variable whose possible values are outcomes of a random phenomenon and assigns a numerical value to each outcome.

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What is the mean of a probability distribution?

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The mean of a probability distribution is the expected value, calculated as the sum of all possible values multiplied by their probabilities.

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How do you calculate the mean of a discrete probability distribution?

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To calculate the mean, multiply each outcome by its probability and sum all the products.

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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, ranging from 0 (impossible) to 1 (certain).

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What does it mean for events to be independent?

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Two events are independent if the occurrence of one does not affect the probability of the other occurring.

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What is the formula for the binomial probability?

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

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What is the variance of a discrete probability distribution?

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The variance measures the spread of a distribution and is calculated as the expected value of the squared deviation from the mean.

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How do you find the variance of a discrete probability distribution?

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To find the variance, calculate the expected value of the squared differences between each outcome and the mean.

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What is a probability mass function (PMF)?

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A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.