A random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$ $3$ $4$
$P (X)$ $0.1$ $k$ $2 k$ $2 k$ $k$
Determine:
(i) $k$
(ii) $P (X \geq 2)$ .

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Solution

(i) Since $\sum P (x) = 1$
$\Rightarrow 0.1 + k + 2 k + 2 k + k = 1$
or $6 k = 1 - 0.1$
$k = \frac{0.9}{6} \Rightarrow k = 0.15$
(ii) $P (x \geq 2) = P (x = 2) + P (x = 3) + P (x = 4)$
$= 2 k + 2 k + k$
$= 5 k = 5 (0.15)$
$P (x \geq 2) = 0.75$ .

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