Discrete Random Variables

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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, often representing counts or whole numbers.

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How do you calculate the mean of a discrete random variable?

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To calculate the mean, multiply each value of the random variable by its probability and sum all these products.

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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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What is a probability distribution?

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

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What are the properties of a valid probability distribution?

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1. All probabilities must be between 0 and 1. 2. The sum of all probabilities must equal 1.

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What is standard deviation in the context of discrete random variables?

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Standard deviation measures the amount of variation or dispersion of a set of values in a probability distribution.

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How do you calculate the standard deviation of a discrete random variable?

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To calculate standard deviation, find the square root of the variance, which is the sum of the squared differences between each value and the mean, weighted by their probabilities.

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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 given range.

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What is a cumulative distribution function (CDF)?

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A cumulative distribution function is a function that describes the probability that a random variable takes on a value less than or equal to a specific value.

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What is the role of probability in statistics?

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Probability is used in statistics to make inferences about populations based on sample data, allowing for predictions and decision-making.