# 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.
n persons receive n hats in a random fashion.
Formula used: By linearity of expectation function,
If $$X_{1},X_{2},...,X_{n}$$ are random variables, then
$$E(X_{1},+X_{2}+,...+X_{n})=E(X_{1})+E(X_{2})+...+ E(X_{n})$$ (2) Explain the rules 3 and 4 in sum of several random variables. Are all infinite random variables necessary continuous?Explain. Independent random variables $$\displaystyle{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ are combined according to the formula $$\displaystyle{L}={3}\cdot{X}_{{{1}}}+{2}\cdot{X}_{{{2}}}$$.
If $$\displaystyle{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ both have a variance of 2.0, what is the variance of L? To know:Distribution of the sum of multinomial random variables.
Covariance of multinomial random variables,
$$COV(N_{i},N_{j})=-mP_{i}P_{j},$$ How can the sample covariance be used to estimate the covariance of random variables? Suppose that $$X_{1}, X_{2}, ..., X_{200}$$ is a set of independent and identically distributed Gamma random variables with parameters $$\alpha = 4, \lambda = 3$$.
Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds. Statistical Literacy When using the F distribution to test variances from two populations, should the random variables from each population be independent or dependent? 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.$$\displaystyle{E}{\left({S}\right)}={10}$$, $$\displaystyle{V}{a}{r}{\left({S}\right)}={12}$$ 