Expected Value And Variance
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Expected Value
The mean or expected value of a discrete distribution is the long-run average of occurrences. We must realize that one trial using a discrete random variable yields only one outcome. however, if the process is repeated long enough, the average of the outcomes are most likely to approach a long-run average, expected value, or mean value. This mean or expected value is computed as follows
μ = E(x) = Σ[x . P(x)]
where,E(x) = long-run average
x = an outcome
P(x) = probability of that outcome
Variance
The variance and standard deviation of discrete distribution are solved for by using the outcomes (x) and probabilities of outcomes [P(x)] in a manner similar to that of computing a mean. in addition, the computation of variance and standard deviations use the mean of the discrete distributions. the formula for computing the variance follows:
σ2 = Σ [(x - μ)2 . P(x)]
where,
x = an outcome
P(x) = probability of given outcome
μ = mean
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x = an outcome
P(x) = probability of given outcome
μ = mean
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