Therefore
or m =
= E (X)
i.e. Mean = E(X) = Expected value.
Also variance (X) = s
x^{2} =
On simplification, we get, the standard deviation,
i.e. s x^{2} =
Example A business can make a profit
of $2000/ with the probability 0.4 or it can have a loss of $1000/
with the probability 0.6. What is the expected profit ?
Solution : The discrete random variable
‘x’ is
x_{1} = $ 2000 (profit)
x_{2} =  $1000 (loss)
With probabilities P_{1} = 0.4 and P_{2} = 0.6 respectively
Then expected profit is given by,
E(x) = P_{1}x_{1}
+ P_{2}x2
= (0.4) (2000) + (0.6) (1000)
= $ 200
Example What is the expected value
of the number of points that will be obtained in a single throw
of an ordinary dice ?
Solution : The discrete random variable
‘x’, in this problem assume values
x_{1} = 1, x_{2} = 2, x_{3} = 3, x_{4} = 4, x_{5} = 5 and x_{6} = 6
With probabilities P_{1} = P_{2} = P_{3} = P_{4} = P_{5} = P_{6} = 1/6 (each)
Expected value of the number of points is given by,
E(x) = P_{1}x_{1} + P_{2} x_{2}
+ P_{3}x_{3} + P_{4} x_{4} + P_{5}
x_{5} + P_{6} x_{6} =
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