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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