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.
$\text{P}(\text{X}=\text{x})=\begin{cases}\text{k}, & \text{if x}=0\\2\text{k}, & \text{if x}=1\\3\text{k}, & \text{if x}=2\\0, & \text{otherwise}\end{cases}$
Determine the value of ‘k’.

✓

Answer

It is known that the sum of probabilities of a probability distribution of random variables is one.
$\therefore\text{k}+2\text{k}+3\text{k}+0=1$
$\Rightarrow6\text{k}=1$
$\Rightarrow\text{k}=\frac{1}{6}$

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