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KIC000014

# KIC000014 - Expected Values Random variables are often...

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Elementary Statistics: A Review Expected Values ); Specifically, the mean of X, denoted Px, is defined by .. Px = E(X) = P,X, + p,X, + ... + P"X .. = LP,X, ;=1 Expected Values );. Random variables are often described in terms of their means and variances, which in turn are defined in terms of the expectations operator E. );. Assume that X" X 2 , ••• , X N represent the N possible outcomes associated with the random variable X. l> Then the mean, or expected value, of X is a weighted average of the possible outcomes, where the probabilities of the outcomes serve as the appropriate weights. where Pi is the probability tbatX, occurs, !:Pi = I, and E( ) is the expectations operator. Expected Values: Variance l> The variance of a random variable provides a measure of the spread, or dispersion, around the mean. );.It is denoted a~ and it is defined as .. Var(X) = 0-; = I>, [X, -E(X)j' r=) );. Thus, the variance is a weighted average of the squares of the deviations of outcomes on X from its expected value, with the corresponding probabilities of each outcome occurring serving as weights.

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