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

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.

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