Consider the following inventory problem - every morning warehouse has 5 units of a certain product. It is known that only 1 out of 3 possible customers can show up during the day and customers can show up with equal probabilities. I.e. each customer can show up with probability 1/3, but only one of them comes to the store. First customer can buy 1 unit of product with probability 3/5 and 2 units with probability 2/5. Second customer can buy 1 unit with probability 3/5, 2 units with probability 1/5, and 4 units with probability 1/5. Third customer can buy 3 units with probability 3/5, 4 units with probability 1/5, and 5 units with probability 1/5.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1
Consider the following inventory problem - every morning warehouse has 5 units of a certain product. It is
known that only 1 out of 3 possible customers can show up during the day and customers can show up with
equal probabilities. I.e. each customer can show up with probability 1/3, but only one of them comes to the
store.
First customer can buy 1 unit of product with probability 3/5 and 2 units with probability 2/5.
Second customer can buy 1 unit with probability 3/5, 2 units with probability 1/5, and 4 units with probability
1/5.
Third customer can buy 3 units with probability 3/5, 4 units with probability 1/5, and 5 units with probability
1/5.
Define random variable X - how many units of product are left at the end of the day.
Compute probability mass function for X.
Sketch cumulative distribution function.
Compute the expected value of X.
Transcribed Image Text:Problem 1 Consider the following inventory problem - every morning warehouse has 5 units of a certain product. It is known that only 1 out of 3 possible customers can show up during the day and customers can show up with equal probabilities. I.e. each customer can show up with probability 1/3, but only one of them comes to the store. First customer can buy 1 unit of product with probability 3/5 and 2 units with probability 2/5. Second customer can buy 1 unit with probability 3/5, 2 units with probability 1/5, and 4 units with probability 1/5. Third customer can buy 3 units with probability 3/5, 4 units with probability 1/5, and 5 units with probability 1/5. Define random variable X - how many units of product are left at the end of the day. Compute probability mass function for X. Sketch cumulative distribution function. Compute the expected value of X.
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