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प्रश्न
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.
उत्तर
The probability distribution of X is given as:
| X: | 0.5 | 1 | 1.5 | 2 |
| P(X): | k | k2 | 2k2 | k |
\[ \text{ Mean } = \sum p_i x_i = 0 . 5 \times k + 1 \times k^2 + 1 . 5 \times 2 k^2 + 2 \times k\]
\[ = 0 . 5 \times \frac{1}{3} + 1 \times \left( \frac{1}{3} \right)^2 + 1 . 5 \times 2 \left( \frac{1}{3} \right)^2 + 2 \times \frac{1}{3}\]
\[ = \frac{0 . 5}{3} + \frac{1}{9} + \frac{3}{9} + \frac{2}{3}\]
\[ = \frac{1 . 5 + 1 + 3 + 6}{9}\]
\[ = \frac{11 . 5}{9}\]
\[ = \frac{115}{90}\]
\[ = \frac{23}{18}\]
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