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At a made-up café, each customer orders 1, 2 or 3 cups of tea with probabilities 0.6, 0.3 and 0.1…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
At a made-up café, each customer orders , or cups of tea with probabilities , and . Find the expected number of cups per customer. How many cups should the café expect to serve to customers?
Need a reminder? The key ideaShow
The expected value is the long-run mean, each value weighted by its probability:
The expected value of a total is the total of the expected values.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The expected value. cups.
Step 2. The total. cups.
Answer: cups per customer, and about cups.
Check. Most customers order one cup, a few order more, so a mean a little above makes sense.
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