Dec 4 - Discrete Probability Distributions

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What is a discrete probability distribution?

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A discrete probability distribution is a statistical function that describes the likelihood of obtaining the possible values that a discrete random variable can take.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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Define a discrete random variable.

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A discrete random variable is a variable that can take on a countable number of distinct values, often representing counts or whole numbers.

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What is the probability mass function (PMF)?

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The probability mass function (PMF) is a function that gives the probability that a discrete random variable is equal to a specific value.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

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The mean (expected value) is calculated by summing the products of each value of the random variable and its corresponding probability.

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What is the variance of a discrete random variable?

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Variance measures the spread of a set of values and is calculated as the expected value of the squared deviation of a random variable from its mean.

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What is the difference between discrete and continuous random variables?

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Discrete random variables can take on a finite or countably infinite number of values, while continuous random variables can take on any value within a given range.

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Provide an example of a discrete random variable.

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The number of students in a classroom is a discrete random variable because it can only take whole number values.

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What is the cumulative distribution function (CDF) for a discrete random variable?

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The cumulative distribution function (CDF) gives the probability that a discrete random variable is less than or equal to a certain value.

Tags

CCSS.HSS.MD.A.2

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What is the significance of the total probability in a discrete probability distribution?

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The total probability of all possible outcomes in a discrete probability distribution must equal 1.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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How do you find the probability of at least k successes in a binomial distribution?

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To find the probability of at least k successes, sum the probabilities of getting k, k+1, ..., up to n successes using the binomial probability formula.