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Mean and Standard Deviation of a Discrete Random Variable

Mean and Standard Deviation of a Discrete Random Variable. Sections 5.3, 5.4. Mean of a Discrete Random Variable. Mean, µ, is also referred to as the expected value of random variable x or E(x) µ = ∑xP(x) or E(x) = ∑xP(x).

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Mean and Standard Deviation of a Discrete Random Variable

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  1. Mean and Standard Deviation of a Discrete Random Variable Sections 5.3, 5.4

  2. Mean of a Discrete Random Variable • Mean, µ, is also referred to as the expected value of random variable x or E(x) • µ = ∑xP(x) or E(x) = ∑xP(x)

  3. Example: Find the mean number of breakdowns of a machine per week.

  4. Standard Deviation of a Discrete Random Variable • Standard Deviation, σ, measures the spread of the possible values of random variable x. • σ = √ ∑ [(x - µ)2 * P(x)] • Shortcut: σ = √ ∑ x2P(x) – µ2

  5. Example: σ = . • Substitute into the formula to find σ.

  6. Example: • The company believes it will earn 4.5 million, 1.2 million, or lose 2.3 million annually depending on sales of a new product. • Probabilities of each are: .32, .51, and .17. • Find the mean and the standard deviation of x.

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