# To Explain:Linearity of expectation of random variables.

Question
Random variables
To Explain:Linearity of expectation of random variables.

2021-01-26
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.

### Relevant Questions

The expectation of the number of people getting their correct hats in the hat check problem, using linearity of expectations.
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Formula used: By linearity of expectation function,
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a.$$\displaystyle{E}{\left({S}\right)}={10}$$, $$\displaystyle{V}{a}{r}{\left({S}\right)}={1.66667}$$
b.$$\displaystyle{E}{\left({S}\right)}={200}$$, $$\displaystyle{V}{a}{r}{\left({S}\right)}={16.6667}$$
c.$$\displaystyle{E}{\left({S}\right)}={100}$$, $$\displaystyle{V}{a}{r}{\left({S}\right)}={200}$$
a.$$\displaystyle{E}{\left({S}\right)}={10}$$, $$\displaystyle{V}{a}{r}{\left({S}\right)}={12}$$