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 P(X ≤ 2) and 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	\[\frac{k}{2}\]	\[\frac{k}{4}\]	\[\frac{k}{8}\]

\[ \text{ As } , P\left( X \leq 2 \right) = 1 - P\left( X = 3 \right)\]
\[ = 1 - \frac{k}{8}\]
\[ = 1 - \frac{8}{15 \times 8}\]
\[ = 1 - \frac{1}{15}\]
\[ = \frac{14}{15}\]
\[\text{ Also} , P\left( X > 2 \right) = P\left( X = 3 \right)\]
\[ = \frac{8}{15 \times 8}\]
\[ = \frac{1}{15}\]