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A made-up computer shop studies its laptops…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up computer shop studies its laptops. In a year, a laptop needs no repair with probability , a repair costing rupees with probability , and a repair costing rupees with probability . The shop sells a repair plan for rupees a year. Find the expected repair cost of one laptop in a year. Find the shop's expected gain on one plan.
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. Expected cost. rupees.
Step 2. Expected gain. rupees.
Answer: rupees and rupees.
What it means. Over many plans the shop gains about rupees each. One customer whose laptop needs the big repair gains rupees. The expected value is about the long run.
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