AP Stats Unit 6 Random Variables

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What is a random variable?

Back

A random variable is a numerical outcome of a random phenomenon. It can be discrete (taking specific values) or continuous (taking any value within a range).

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What is the expected value of a random variable?

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The expected value (mean) of a random variable is the long-term average of its possible values, weighted by their probabilities.

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How do you calculate the expected number of trials until the first success in a Bernoulli process?

Back

The expected number of trials until the first success is given by 1/p, where p is the probability of success.

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What is the probability distribution of a discrete random variable?

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A probability distribution of a discrete random variable lists all possible values and their corresponding probabilities.

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What is the standard deviation of a random variable?

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The standard deviation measures the dispersion or spread of a set of values around the mean. It indicates how much the values typically differ from the mean.

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What does it mean if a random variable has a standard deviation of 0.9?

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It means that the values of the random variable typically differ from the mean by about 0.9 units.

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How do you find the mean of a binomial distribution?

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The mean of a binomial distribution is calculated as n * p, where n is the number of trials and p is the probability of success.

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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 given by n * p * (1 - p), where n is the number of trials and p is the probability of success.

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What is the significance of the Central Limit Theorem in statistics?

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

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What is a cumulative distribution function (CDF)?

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