Question

Consider two independent random variables: $X ∼ N(5, 4)$ and $Y~N(3, 2)$. If $(2X + 3Y)~N(\mu, \sigma ^2)$, then the values of mean ($\mu$) and variance ($\sigma ^2$) are

• A. $\mu$ = 19 and $\sigma ^2$ = 34
• B. $\mu$ = 8 and $\sigma ^2$ = 14
• C. $\mu$ = 19 and $\sigma ^2$ = 14
• D. $\mu$ = 8 and $\sigma ^2$ = 34

Answer 1

Answer: (A)

$\mu$ = 19 and $\sigma ^2$ = 34

Answer 2

The correct answer is (A) :$\mu$ = 19 and $\sigma ^2$ = 34