Expected Value And Variance Assignment Help | Expected Value And Variance Homework Help

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:

σ2Σ [(x - μ)2 . P(x)]

where,
      x = an outcome
 P(x) = probability of given outcome
     μ  = mean

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