Probability Distributions

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What is a probability distribution?

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

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the mean of a binomial distribution?

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The mean of a binomial distribution is calculated using the formula: Mean (μ) = n * p, where n is the number of trials and p is the probability of success.

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CCSS.HSS.ID.A.4

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What is a discrete random variable?

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A discrete random variable is a type of variable that can take on a countable number of distinct values, such as the number of siblings a person has.

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CCSS.6.SP.A.1

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What is a continuous random variable?

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A continuous random variable is a variable that can take on an infinite number of values within a given range, such as height or weight.

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How do you calculate the mean of a set of data?

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To calculate the mean, sum all the values in the data set and divide by the number of values.

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CCSS.6.SP.B.5C

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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 and 1.

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CCSS.7.SP.C.5

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What is the formula for the variance of a binomial distribution?

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The variance of a binomial distribution is calculated using the formula: Variance (σ²) = n * p * (1 - p).

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What does it mean if a random variable is normally distributed?

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If a random variable is normally distributed, it means that the values are symmetrically distributed around the mean, forming a bell-shaped curve.

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CCSS.HSS.ID.A.4

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

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What is the difference between independent and dependent events?

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Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.

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CCSS.HSS.CP.A.5