MEAN AND VARIANCE OF PROBABILITY DISTRIBUTION

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What is the mean of a probability distribution?

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The mean of a probability distribution, also known as the expected value, is the sum of all possible values, each multiplied by its probability of occurrence.

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What is the variance of a probability distribution?

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The variance of a probability distribution measures the spread of the distribution. It is calculated as the expected value of the squared deviation of a random variable from its mean.

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

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To calculate the mean of a discrete probability distribution, multiply each possible value by its probability and sum all the products.

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What is a discrete probability distribution?

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A discrete probability distribution is a probability distribution that shows the probabilities of outcomes with finite values.

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What is the relationship between mean and variance in a probability distribution?

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The mean provides a measure of central tendency, while the variance provides a measure of dispersion around that mean.

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What is the formula for calculating variance in a discrete probability distribution?

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Variance = Σ [ (x - μ)² * P(x) ], where μ is the mean, x is each value, and P(x) is the probability of x.

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What does it mean if a probability distribution is skewed?

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A skewed probability distribution is one where the probabilities are not symmetrically distributed around the mean, indicating that one tail is longer or fatter than the other.

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What is the total probability in a probability distribution?

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The total probability in a probability distribution must equal 1, as it represents the certainty that one of the possible outcomes will occur.

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How do you find the probability of an event in a probability distribution?

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To find the probability of an event, sum the probabilities of all outcomes that correspond to that event.

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What is the significance of the expected value in probability distributions?

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The expected value represents the long-term average outcome of a random variable over many trials.