Exact sampling distribution of a sample proportion
A finite population contains \(7\) devices. \(5\) are classified as successes and \(2\) as failures
A sample of \(n=3\) is selected without replacement. Let \(X\) be the number of successes in the sample
\[\hat p=\frac{X}{n}\]
The complete table below gives the possible values of \(X\) and the sample proportion
| \(x\) | \(\hat p\) | Number of samples | Probability |
|---|---|---|---|
| \(1\) | \(\frac{1}{3}\) | \(5\) | \(\frac{1}{7}\) |
| \(2\) | \(\frac{2}{3}\) | \(20\) | \(\frac{4}{7}\) |
| \(3\) | \(1\) | \(10\) | ? |