- Page 1 and 2: Random Variables and Discrete Proba
- Page 3 and 4: Random Variable • A random variab
- Page 5: Random Variable • A discrete rand
- Page 9 and 10: Random Variable • A discrete rand
- Page 11 and 12: Random Variable • A continuous ra
- Page 13 and 14: Random Variable • A continuous ra
- Page 15 and 16: Random Variable • A continuous ra
- Page 17 and 18: Probability Distribution for a Disc
- Page 19 and 20: Probability Distribution for a Disc
- Page 21 and 22: Probability Distribution for a Disc
- Page 23 and 24: Probability Distribution for a Disc
- Page 25 and 26: What is the probability distributio
- Page 27 and 28: What is the probability distributio
- Page 29 and 30: What is the probability distributio
- Page 31 and 32: What is the probability distributio
- Page 33 and 34: What is the probability distributio
- Page 35 and 36: What is the probability distributio
- Page 37 and 38: What is the probability distributio
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- Page 41 and 42: What is the probability distributio
- Page 43 and 44: What is the probability distributio
- Page 45 and 46: 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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Does the table below represent a pr
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Does the table below represent a pr
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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 • Next, we determi
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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 • Alternate Altern
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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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Expected Value for a Discrete Rando
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Expected Value for a Discrete Rando
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Expected Value for a Discrete Rando
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How many Heads should we expect if
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How many Heads should we expect if
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How many Heads should we expect if
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What is the expected value for the
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What is the expected value for the
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What is the expected value for the
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What is the expected prize for our
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What is the expected prize for our
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What is the expected prize for our
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What are the expected winnings for
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What are the expected winnings for
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What are the expected winnings for
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For our raffle example, can we use
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For our raffle example, can we use
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For our raffle example, can we use
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Variance and Standard Deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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What is the standard deviation for
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Variance and Standard Deviation for