## Related questions with answers

An investment in company A has an expected return of $\$ 30,000$ with a standard deviation of $\$ 4000$. An investment in company B has an expected return of $\$ 45,000$ with a standard deviation of $\$ 3000$. If investments are made in both companies, what are the expectation and standard deviation of the total return?

Solution

VerifiedLet $\color{#c34632}{X_A}$ represents $\textit{the return}$ if the money is invested in company A, $\color{#c34632}{X_B}$ represents $\textit{the return}$ if the money is invested in company B, and $T$ represents $\textbf{the total}$ return. Then,

${\color{Brown}{T=X_A+X_B}}$

For these two,clearly, $\color{#c34632}{\text{independent}}$ random variables $X_A$ and $X_B$, from the task, we have

$\mu_A=E(X_A)=30000\,,\,\sigma_A=\sqrt{\mathrm{Var}(X_A)}=4000$

$\mu_B=E(X_B)=45000\,,\,\sigma_B=\sqrt{\mathrm{Var}(X_B)}=3000$

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