3. The discrete random variable \(X\) has the probability distribution given below.
| \(x\) | 2 | 4 | 7 | \(k\) |
| \(\mathrm { P } ( X = x )\) | 0.05 | 0.15 | 0.3 | 0.5 |
- Find the mean of \(X\) in terms of \(k\).
- Find the bias in using ( \(2 \bar { X } - 5\) ) as an estimator of \(k\).
Fifty observations of \(X\) were made giving a sample mean of 8.34 correct to 3 significant figures.
- Calculate an unbiased estimate of \(k\).
(2 marks)