Concept explainers
In Exercise 5.38, we determined that the joint density
In this case, the random variable Y1 − Y2 measures the amount of stock remaining at the end of the week, a quantity of great importance to the supplier. Find E(Y1 − Y2).
5.38 Let Y1 denote the weight (in tons) of a bulk item stocked by a supplier at the beginning of a week and suppose that Y1 has a uniform distribution over the interval 0 ≤ y1 ≤ 1. Let Y2 denote the amount (by weight) of this item sold by the supplier during the week and suppose that Y2 has a uniform distribution over the interval 0 ≤ y2 ≤ y1, where y1 is a specific value of Y1.
- a Find the joint density function for Y1 and Y2.
- b If the supplier stocks a half-ton of the item, what is the probability that she sells more than a quarter-ton?
- c If it is known that the supplier sold a quarter-ton of the item, what is the probability that she had stocked more than a half-ton?
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Mathematical Statistics with Applications
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