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 outcomes of a discrete random variable, which can take on a countable number of values.

Tags

CCSS.HSS.MD.A.4

CCSS.HSS.MD.A.3

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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 multiplying each possible value by its probability and summing the results: E(X) = Σ [x * P(x)].

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CCSS.HSS.MD.A.2

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What is the expected value in probability?

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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.

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CCSS.HSS.MD.A.2

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Define variance in the context of probability distributions.

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Variance measures the spread of a set of values in a probability distribution, calculated as the average of the squared differences from the mean.

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What is the formula for calculating variance of a discrete random variable?

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Variance (σ²) = Σ [(x - μ)² * P(x)], where μ is the mean.

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Explain the concept of standard deviation in probability.

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Standard deviation is the square root of the variance and provides a measure of the amount of variation or dispersion in a set of values.

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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).

Tags

CCSS.7.SP.C.5

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How do you find the probability of multiple independent events occurring?

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For independent events, the probability of all events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

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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.

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What does it mean for a distribution to be binomial?

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A binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.