The random variable X has a probability distribution P(X) of the … - Vidyadip

Question

The random variable $X$ has a probability distribution $P(X)$ of the following form, where k is some number:
$P(X)=\left\{\begin{array}{l}k, \text { if } x=0 \\ 2 k, \text { if } x=1 \\ 3 k, \text { if } x=2 \\ 0, \text { otherwise }\end{array}\right.$
(i) Find the value of $k$
(ii) Find $P(X < 2)$

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Answer

Here,
(i) Since $P(0) + P(1) + P(2) = 1,$ we have
$k + 2k + 3k = 1$
$\text{i.e., } 6k = 1, \text{ or } k = \frac{1}{6}.$
(ii) $P(X < 2) = P(0) + P(1)$
$= k + 2k = 3k = \frac{1}{2}.$

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