4.14 Linear combinations of random variables and unbiased estimates Quiz

1. $E(X)=5$. Find $E(3X-2)$.

• A. $15$
• B. $17$
• C. $13$
• D. $11$

2. $X$ and $Y$ are independent with $Var(X)=4$ and $Var(Y)=9$. Find $Var(X-Y)$.

• A. $5$
• B. $13$
• C. $-5$
• D. $36$

3. A sample of $n=10$ has $s_n^2=2.4$. Find the unbiased estimate of the population variance.

• A. $2.67$
• B. $2.40$
• C. $2.16$
• D. $2.00$

4. Which statement about $\bar x$ is correct?

• A. It underestimates $\mu$ on average
• B. It overestimates $\mu$ on average
• C. It equals $\mu$ exactly
• D. It is an unbiased estimate of $\mu$

5. $X_1$ and $X_2$ are independent copies of $X$ with variance $\sigma^2$. Which is correct?

• A. $Var(2X)=Var(X_1+X_2)=2\sigma^2$
• B. $Var(2X)=4\sigma^2$ and $Var(X_1+X_2)=2\sigma^2$
• C. $Var(2X)=Var(X_1+X_2)=4\sigma^2$
• D. $Var(2X)=2\sigma^2$ and $Var(X_1+X_2)=4\sigma^2$