Random Variables and Discrete Probability Distributions

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Expected Value for a Discrete Random Variable • The mean of a discrete random variable X, denoted μX, , also referred to as the expected value. • We can think of μX = E(X) as the mean value of a very large (infinite, if we could) number of repetitions of the experiment in which the values of X occur in proportions equivalent to the probabilities of X.
Expected Value for a Discrete Random Variable • We can think of μX = E(X) as the average value of the random variable that we would expect to obtain if we perform the experiment repeatedly. �� Letting xk represent the outcome of the k th repetition of the experiment, [x 1 + x 2 + … + xk + … + xn]/n ]/n gets closer to μX = E(X) as the number of repetitions of the experiment, n, increases in value.
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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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Page 67 and 68: Notation • For clarity, we will u
Page 69 and 70: 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
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Page 111 and 112: 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
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Variance and Standard Deviation for
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Random Variables and Discrete Probability Distributions

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