jee-main 2025 Q69

jee-main · India · session2_02apr_shift2 Measures of Location and Spread
Q69. If the mean of the following probability distribution of a random variable $X$ :
X02468
$\mathrm { P } ( \mathrm { X } )$$a$$2 a$$a + b$$2 b$$3 b$

is $\frac { 46 } { 9 }$, then the variance of the distribution is
(1) $\frac { 173 } { 27 }$
(2) $\frac { 566 } { 81 }$
(3) $\frac { 151 } { 27 }$
(4) $\frac { 581 } { 81 }$
Q69. If the mean of the following probability distribution of a random variable $X$ :

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
X & 0 & 2 & 4 & 6 & 8 \\
\hline
$\mathrm { P } ( \mathrm { X } )$ & $a$ & $2 a$ & $a + b$ & $2 b$ & $3 b$ \\
\hline
\end{tabular}
\end{center}

is $\frac { 46 } { 9 }$, then the variance of the distribution is\\
(1) $\frac { 173 } { 27 }$\\
(2) $\frac { 566 } { 81 }$\\
(3) $\frac { 151 } { 27 }$\\
(4) $\frac { 581 } { 81 }$