Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable $$X _ { 1 } + X _ { 2 }$$ $$\begin{array} { c | c c }
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 14 & 3 \
\mathrm { Y } & 60 & 8
\end{array}$$
A)? = 28,? = 4.24
B)? = 74,? = 8.54
C)? = 28,? = 6
D)? = 28,? = 2.45
E)? = 74,? = 11

Question

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable $$X _ { 1 } + X _ { 2 }$$ $$\begin{array} { c | c c } 
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 14 & 3 \
\mathrm { Y } & 60 & 8
\end{array}$$
A)? = 28,? = 4.24
B)? = 74,? = 8.54
C)? = 28,? = 6
D)? = 28,? = 2.45
E)? = 74,? = 11

Quizplus · Accepted Answer

The mean of the sum of independent random variables is the sum of their means, and the standard deviation of the sum is the square root of the sum of their variances. Therefore, the mean of $X_1 + X_2$ is $14 + 60 = 74$, and the standard deviation is $\sqrt{3^2 + 8^2} = 8.54$.

Given Independent Random Variables with Means and Standard Deviations as Shown,find