## 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 followsμ = E(

where,*x*) = Σ[*x*. P(*x*)]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:**σ**Σ [(x - μ)

^{2}=^{2}. P(

*x*)]

where,

P(

μ = mean

# For more help in

*x*= an outcomeP(

*x*) = probability of given outcomeμ = mean

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