csat-suneung 2011 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.
$X$- 1012Total
$\mathrm { P } ( X = x )$$\frac { 3 - a } { 8 }$$\frac { 1 } { 8 }$$\frac { 3 + a } { 8 }$$\frac { 1 } { 8 }$1

When $\mathrm { P } ( 0 \leqq X \leqq 2 ) = \frac { 7 } { 8 }$, what is the value of the expected value $\mathrm { E } ( X )$ of the random variable $X$? [3 points]
(1) $\frac { 1 } { 4 }$
(2) $\frac { 3 } { 8 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 5 } { 8 }$
(5) $\frac { 3 } { 4 }$
The probability distribution table of the random variable $X$ is as follows.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$X$ & - 1 & 0 & 1 & 2 & Total \\
\hline
$\mathrm { P } ( X = x )$ & $\frac { 3 - a } { 8 }$ & $\frac { 1 } { 8 }$ & $\frac { 3 + a } { 8 }$ & $\frac { 1 } { 8 }$ & 1 \\
\hline
\end{tabular}
\end{center}

When $\mathrm { P } ( 0 \leqq X \leqq 2 ) = \frac { 7 } { 8 }$, what is the value of the expected value $\mathrm { E } ( X )$ of the random variable $X$? [3 points]\\
(1) $\frac { 1 } { 4 }$\\
(2) $\frac { 3 } { 8 }$\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 5 } { 8 }$\\
(5) $\frac { 3 } { 4 }$