84 specimen copies of soft coal, sampled from the ongoing production in a colliery over a period of 7 days, had been analyzed with regard to ash and water content, respectively [in \%]. Both ash and water content have been partitioned into 6 classes. The table shows the results:

Let \(X\) be the water content and \(Y\) be the ash content of a randomly chosen specimen copy out of the 84 ones. Since the originally measured values are not given, it is assumed that the values, which \(X\) and \(Y\) can take on, are the centers of the given classes, i.e., \(16.5,17.5, \cdots, 21.5\).
(1) Draw the distribution functions of \(X\) and \(Y\).
(2) Determine \(E(X), \operatorname{Var}(X), E(Y)\), and \(\operatorname{Var}(Y)\).

Transcribed Image Text:

water [16, 17) [17, 18) [18, 19) [19, 20] [20, 21) [21,22] [23, 24) 0 0 1 1 2 4 [24, 25) 0 1 3 4 3 3 ash [25, 26) 0 2 8 7 2 1 [26, 27) 1 4 10 8 1 0 [27, 28) 0 5 4 4 0 0 [28, 29) 2 0 1 0 1 0