csat-suneung 2010 Q8

csat-suneung · South-Korea · csat__math-humanities 3 marks Discrete Probability Distributions Probability Distribution Table Completion and Expectation Calculation
The probability distribution table of the random variable $X$ is as follows.
$X$012Total
$\mathrm { P } ( X = x )$$\frac { 2 } { 7 }$$\frac { 3 } { 7 }$$\frac { 2 } { 7 }$1

What is the value of the variance $\mathrm { V } ( 7 X )$ of the random variable $7 X$? [3 points]
(1) 14
(2) 21
(3) 28
(4) 35
(5) 42
The probability distribution table of the random variable $X$ is as follows.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$X$ & 0 & 1 & 2 & Total \\
\hline
$\mathrm { P } ( X = x )$ & $\frac { 2 } { 7 }$ & $\frac { 3 } { 7 }$ & $\frac { 2 } { 7 }$ & 1 \\
\hline
\end{tabular}
\end{center}

What is the value of the variance $\mathrm { V } ( 7 X )$ of the random variable $7 X$? [3 points]\\
(1) 14\\
(2) 21\\
(3) 28\\
(4) 35\\
(5) 42