The probability distribution of $X$ is
$X$ 0 1 2 3
$P (x)$ 0.3 k 2k 3k
The value of $k$ is

0.116

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0.7

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1

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0.3

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Solution

The correct option is A $0.116$
$\infty \sum x = 0 P (x) = 1$

$3 \sum x = 0 P (x) = 1$
$P (0) + P (1) + P (2) + P (3) = 1$
$\Rightarrow 0.3 + k + 2 k + 3 k = 1$
$\Rightarrow 6 k = 1 - 0.3$
$\Rightarrow 6 k = 0.7$
$k = \frac{0.7}{6};$ $k = 0.116$

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