We choose a number from the set $\{0,...,9999\}$ randomly, and denote by $X$ the sum of its digits. Find the expected value of $X$.
If we are letting $X$ be in the sum of digits, you can specify $X=a+b+c+d$ for $0\le a,b,c,d,<10$ with $0 \le X \le 36.$ I think I am supposed to use indicators, but can't seem to define what a success would be among picking digits, and the relation to the sum.
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$\begingroup$Hint: By Linearity of Expectation, $\mathbb{E}[X] = \mathbb{E}[a+b+c+d] = \mathbb{E}[a]+\mathbb{E}[b]+\mathbb{E}[c]+\mathbb{E}[d]$.
Can you work out the expected value of each digit?
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