Question

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	k	k2	2k2	k

Determine the mean of the distribution.                

Answer 1

The probability distribution of X is given as: 

X:	0.5	1	1.5	2
P(X):	k	k2	2k2	k

\[  \text{ Mean } = \sum p_i x_i = 0 . 5 \times k + 1 \times k^2 + 1 . 5 \times 2 k^2 + 2 \times k\]
\[ = 0 . 5 \times \frac{1}{3} + 1 \times \left( \frac{1}{3} \right)^2 + 1 . 5 \times 2 \left( \frac{1}{3} \right)^2 + 2 \times \frac{1}{3}\]
\[ = \frac{0 . 5}{3} + \frac{1}{9} + \frac{3}{9} + \frac{2}{3}\]
\[ = \frac{1 . 5 + 1 + 3 + 6}{9}\]
\[ = \frac{11 . 5}{9}\]
\[ = \frac{115}{90}\]
\[ = \frac{23}{18}\]