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

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What is a continuous probability distribution?

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A continuous probability distribution is a statistical distribution that describes the likelihood of outcomes for a continuous random variable, which can take on an infinite number of values within a given range.

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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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What is standard deviation in the context of probability distributions?

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Standard deviation measures the amount of variation or dispersion in a set of values. In probability distributions, it quantifies how much the values deviate from the mean.

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What is the formula for standard deviation of a discrete probability distribution?

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The standard deviation is calculated using the formula: σ = √(Σ [P(x) * (x - μ)²]), where μ is the mean.

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What is a random variable?

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A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

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What is the difference between a discrete and a continuous random variable?

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A discrete random variable can take on a finite or countable number of values, while a continuous random variable can take on an infinite number of values within a range.

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What is a probability mass function (PMF)?

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A PMF is a function that gives the probability that a discrete random variable is exactly equal to some value.

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What is a probability density function (PDF)?

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A PDF is a function that describes the likelihood of a continuous random variable taking on a particular value, where the area under the curve represents probabilities.

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What does it mean for a distribution to be valid?

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A probability distribution is valid if the sum of all probabilities equals 1 and each individual probability is between 0 and 1.