Chapter 8 Random Variables and Probability Models.pdf -...

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8.1 - Expected value of a Random Variable Random Variable - Value is based on the outcome of a random event Denoted by a capital letter X Particular value is denoted by lowercase letter x Discrete Random Variable - When all outcomes of a random variable can be listed Continuous Random Variable - A random variable that can take on any value (possibly bounded on one or both sides) Probability Model - The collection of all the possible values an the probabilities associated with them for the random variable Parameter - Expected value of a policy Expected Value ࠵? ( ࠵? ) = ∑࠵?࠵? ( ࠵? ) 8.2 - Standard Deviation of a Random Variable Standard Deviation is calculated by first computing the deviation of each data value from the mean and square it Variance - the expected value of those squared deviations ( ࠵?࠵?࠵?࠵?࠵? ) . = ࠵?࠵?࠵? ( ࠵? ) = ∑ ( ࠵? − µ ) . ࠵? ( ࠵? ) ( ࠵?࠵?࠵?࠵?࠵? ) = ࠵?࠵? ( ࠵? ) = 6࠵?࠵?࠵? ( ࠵? ) 8.3 - Properties of Expected Values and Variances ࠵? ( ࠵? ± ࠵? ) = ࠵? ( ࠵? ) ± ࠵? ࠵?࠵?࠵? ( ࠵? ± ࠵? ) = ࠵?࠵?࠵? ( ࠵? ) ࠵?࠵? ( ࠵? ± ࠵? ) = ࠵?࠵?

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