For the weekly demand of the certain juice in the thousand of liters for the convenience store chain has the continuous random variable of f(x) = x2 + x – 2, and the x has the density function of;

                        f(x) = {2(x-1),0      1< x < 2 elsewhere

Determine fro the expected value of the weekly demand of the drink?

Solution:

From the theorem:

            E (x2 + x – 2) = E (x2) + E(x) – E(2)

E (2) = 2 which has the direct integration of

E(x) = ∫21 2x(x-1)  dx

       = 2∫21 (x2 – x) dx = 5/3

And

E(x2) = 2∫21 (x2 – 1) dx

         = 2∫21 (x3 – x2) dx

         = 17/6

Now,

E (x2 + x – 2)

         = 17/6 + 5/3 2

         = 5/2

This means that the average demand per week for the juice drink in the efficiency stores is 2500 liters.






Credit:ivythesis.typepad.com


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