Question

The probability distribution of a random variable X is given below:

x	0	1	2	3
P(X)	k	\[\frac{k}{2}\]	\[\frac{k}{4}\]	\[\frac{k}{8}\]

Determine the value of k .

Answer 1

We have,
The probability distribution of a random variable X is given below:

x	0	1	2	3
P(X)	k	\[\frac{k}{2}\]	\[\frac{k}{4}\]	\[\frac{k}{8}\]

\[ \text{ As } , \sum p_i = 1\]
\[ \Rightarrow k + \frac{k}{2} + \frac{k}{4} + \frac{k}{8} = 1\]
\[ \Rightarrow \frac{8k + 4k + 2k + k}{8} = 1\]
\[ \Rightarrow \frac{15k}{8} = 1\]
\[ \therefore k = \frac{8}{15}\]