If \( \mathrm{X} \) is a random-variable with probability distribution as given below: \( \begin...

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If \( \mathrm{X} \) is a random-variable with probability distribution as given below:
\( \begin{array}{rrrrr}X=x_{i}: & 0 & 1 & 2 & 3 \\ P\left(X=x_{i}\right): & k & 3 k & 3 k & k\end{array} \)
The value of \( k \) and its variance are
(A) \( 1 / 8,22 / 27 \)
(B) \( 1 / 8,23 / 27 \)
(C) \( 1 / 8,24 / 27 \)
(D) \( 1 / 8,3 / 4 \)
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