Random Variables and Discrete Probability Distributions

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Probability Distribution for a Discrete Random Variable • Since all the probabilities associated with the values of the random variable are specified by the probability distribution, the sum of these probabilities must be one. �� Alternate: Alternate: Letting P(X = x) denote the probability that the value of the random variable X is equal to x, these probabilities must be such ∑ P(X = x) = 1
Probability Distribution for a Discrete Random Variable • Requirements for a probability distribution for a discrete random variable �� For P(x) P(x) the probability that the value of the random variable X is equal to x, the following must be true: �� 0 ≤ P(x) P(x) ≤ 1 �� ∑ P(x) P(x) = 1
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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 • 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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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 prize for our
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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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Variance and Standard Deviation for
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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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