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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What is a continuous random variable?

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A continuous random variable can take on an infinite number of values within a given range, often representing measurements.

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How do you calculate the expected value of a discrete random variable?

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The expected value (E[X]) is calculated by summing the products of each value of the random variable and its corresponding probability: E[X] = Σ (x * P(X=x)).

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What is a probability distribution?

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A probability distribution describes how the probabilities are distributed over the values of the random variable.

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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 the expected value of the random variable X given the probabilities: P(X=50)=0.1, P(X=20)=0.3, P(X=5)=0.6?

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E[X] = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 14.

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What is the mean of a probability distribution?

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The mean of a probability distribution is the expected value, representing the average outcome of the random variable.

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Identify whether the following is a discrete or continuous random variable: The number of students in a classroom.

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Discrete Random Variable.

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Identify whether the following is a discrete or continuous random variable: The height of students in a classroom.

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Continuous Random Variable.

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What is the formula for variance of a discrete random variable?

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Variance (Var[X]) = Σ ((x - E[X])^2 * P(X=x)).