Mathematics, 28.12.2019 06:31 tyrone6410
There are 10 balls in an urn, numbered from 1 to 10. if 5 balls are selected at random and their numbers are added, what is the expected value of the total?
Answers: 3
denote the value on the 
-th drawn ball. We want to find the expectation of 
, which by linearity of expectation is![E[S]=E\left[\displaystyle\sum_{i=1}^5B_i\right]=\sum_{i=1}^5E[B_i]](/tpl/images/0435/5394/b1d5b.png)
are independent!)
![E[X_i]=\displaystyle\sum_{i=1}^{10}x\,P(X_i=x)=\frac1{10}\frac{10(10+1)}2=5.5](/tpl/images/0435/5394/e6942.png)
![E[S]=5(5.5)=\boxed{27.5}](/tpl/images/0435/5394/90c49.png)
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There are 10 balls in an urn, numbered from 1 to 10. if 5 balls are selected at random and their num...
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