Expected Value Statistics

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Definition: - The expected value of a discrete random variable x is the value that is expected to occur per repetition, on average, if an experiment is repeated a large number of times. It is denoted by E(x) and calculated as

E(x)= ∑x P(x)

The expected value is also known as mean and is denoted by µ; that is

µ=∑ x P(x)

Example:- Below the probability distribution table where x represents the number of breakdowns for a machine during a given week, and P(x) is the probability of the corresponding value of x


 
x P(x)
0 0.15
1 0.20
2 0.35
3 0.30
 
To find the expected value of breakdowns per week for this machine, we multiply each value of x by its probability and these products. This sum gives the mean of the probability distribution of x. The products x P(x) are listed in the third column of the below table. The sum of these products give ∑x P(x) which is the expected value of x.

Calculating the expected value for the probability distribution of breakdowns.

 
X P(x) x P(x)
0 0.15 0*0.15= 0
1 0.20 1*0.20= 0.20
2 0.35 2*0.35= 0.70
3 0.30 3*0.30= 0.90
    ∑ x P(x)=1.80
 
The expected value is E(x)= 1.80

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