Question

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

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

 Find P(X ≤ 2) + P(X > 2) .

 

Answer 1

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

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

\[ P\left( X \leq 2 \right) + P\left( X > 2 \right)\]
\[ = \frac{14}{15} + \frac{1}{15} \left[ \text.........{ \text{ Using } }  \left( ii \right) \right]\]
\[ = \frac{15}{15}\]
\[ = 1\]