Random Variables and Discrete Probability Distributions

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What is the standard deviation for the number of Heads for the toss of two fair coins? • Or, using the other formula,
What is the standard deviation for the number of Heads for the toss of two fair coins? • we can calculate the standard deviation, again. �� σ2 X = [(0) 2 ·(¼) ) + (1) 2 ·(½) ) + (2) 2 ·(¼)] )] – (1) = [½ [ + 1] - 1 = ½ �� σX = √(½) ≈ 0.707 Heads (1) 2
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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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Raffle Example • Combining this i
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Raffle Example • Note: The point
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Raffle Example • Did you notice t
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Raffle Example • Did you notice t
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Expected Value for a Discrete Rando
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Page 119 and 120: How many Heads should we expect if
Page 125 and 126: What is the expected value for the
Page 131 and 132: What is the expected prize for our
Page 137 and 138: What are the expected winnings for
Page 143 and 144: For our raffle example, can we use
Page 149 and 150: Variance and Standard Deviation for
Page 151 and 152: What is the standard deviation for
Page 163: What is the standard deviation for
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Random Variables and Discrete Probability Distributions

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