To Explain:Linearity of expectation of random variables.

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Consider a set of 20 independent and identically distributed uniform random variables in the interval (0,1). What is the expected value and variance of the sum, S, of these random variables?
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Answer 1

Given:
n random variables \(X_{1},X_{2},....,X_{n}\)
Formula used:
\(E(X_{1},+ X_{2},...,+ X_{n})=E(X_{1})+E(X_{2})+...+E(X_{n})\)
Linearity means additivity over the variables. Thus (1) expresses the fact that expectation is additive over the random variables, in other words, expectation is a linear function.

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To Explain:Linearity of expectation of random variables.

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