7 A company is searching for oil reserves. The company has purchased the rights to make test drillings at four sites. It investigates these sites one at a time but, if oil is found, it does not proceed to any further sites. At each site, there is probability 0.2 of finding oil, independently of all other sites. The random variable \(X\) represents the number of sites investigated. The probability distribution of \(X\) is shown below.

1. Find the expectation and variance of \(X\).
2. It costs \(\pounds 45000\) to investigate each site. Find the expected total cost of the investigation.
3. Draw a suitable diagram to illustrate the distribution of \(X\).