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+4 votes
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asked in general by (270 points)  
If x is the number that comes up when you roll a 20 sided die. What is the expected value of x?
  

1 Answer

+1 vote
answered by (116k points)  

Assign a number to each of those events (having 1 as outcome, having 2 as outcome, ..., having 20 as outcome) which is the job of Random Variable. For this specific example, we can assign the same numbers. The Expected Value equation is μ=x.p(x). Now you have x=1,2,...,20, and if you have p(x), you can easily calculate expected value. 

In this case that we have a fair die with 20 sides, probability of each side is 120. Now, we can calculate it in this way:

μ=x.p(x)=20x=1x.120=12020x=1x=12020×212=10.5

(note: nx=1x=n×(n+1)2)

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