Random Variables and Discrete Probability Distributions

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Variance and Standard Deviation for a Discrete Random Variable • The variance of a discrete random variable X, denoted σ2 X = Var(X), Var(X), is determined using the formula σ2 X = Var(X)= Var(X)= ∑[( [(x x – μX) 2 · P(X = x)] = ∑[x2 · P(X = x)] – (μX ) 2 • The standard deviation of a discrete random variable X, denoted σX, , is the square root of the variance.
What is the standard deviation for the number displayed on the top face of a fair die?
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Random Variables and Discrete Proba
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Random Variable • A random variab
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Random Variable • A discrete rand
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Random Variable • A continuous ra
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Probability Distribution for a Disc
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What is the probability distributio
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Did you notice that each example me
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Requirements for a probability dist
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Requirements for a probability dist
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Did you notice that if the examples
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Did you notice that if the examples
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Notation • For clarity, we will u
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Does the table below represent a pr
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Probability Histogram • As with a
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Raffle Example • Although there a
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Raffle Example • Since not not wi
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Raffle Example • Next, we determi
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Raffle Example • Finally, we comp
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Raffle Example Probability Distribu
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Raffle Example • We do not need t
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Raffle Example • Winnings Winning
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Raffle Example • Alternate Altern
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Random Variables and Discrete Probability Distributions

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