Random Variables and Discrete Probability Distributions

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How many Heads should we expect if we toss two fair coins? <strong>Probability</strong> Distribution for the Toss of Two Fair Coins x P(X = x) 0 ¼ 1 ½ 2 ¼
How many Heads should we expect if we toss two fair coins? • Finally, having determined the probability distribution, we can calculate the expected number of Heads, that is, the expected value for the number of Heads. μX = E(X) = 0·(¼) 0 ) + 1·(½) 1 ) + 2·(¼) 2 ) = ½ + ½ = 1
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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
Page 71 and 72: Does the table below represent a pr
Page 77 and 78: Probability Histogram • As with a
Page 79 and 80: Raffle Example • Although there a
Page 81 and 82: Raffle Example • Since not not wi
Page 83 and 84: Raffle Example • Next, we determi
Page 89 and 90: Raffle Example • Finally, we comp
Page 91 and 92: Raffle Example Probability Distribu
Page 93 and 94: Raffle Example • We do not need t
Page 95 and 96: Raffle Example • Winnings Winning
Page 97 and 98: Raffle Example • Alternate Altern
Page 103 and 104: Raffle Example • Combining this i
Page 105 and 106: Raffle Example • Note: The point
Page 107 and 108: Raffle Example • Did you notice t
Page 109 and 110: Raffle Example • Did you notice t
Page 111 and 112: Expected Value for a Discrete Rando
Page 119 and 120: How many Heads should we expect if
Page 121: 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 167: Variance and Standard Deviation for
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Random Variables and Discrete Probability Distributions

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