In a certain mathematics class, the probabilities have been empirically determined for various numbers of absentees on any given day. These values are shown in the table. Find the expected number of absentees on a given day.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline Prumber absent & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline Prowa & 0.01 & 0.06 & 0.11 & 0.27 & 0.35 & 0.13 & 0.07 \\
\hline
\end{tabular}

The expected number of absentees on a given day is (Round to two decimal places as needed.)

Step 1 ：In a certain mathematics class, the probabilities have been empirically determined for various numbers of absentees on any given day. These values are shown in the table. Find the expected number of absentees on a given day.

Step 2 ：The expected value of a random variable is the sum of the product of each outcome and its probability. In this case, the random variable is the number of absentees on a given day, and the outcomes are the numbers 0 through 6. The probabilities of these outcomes are given in the table.

Step 3 ：So, to find the expected number of absentees, we need to multiply each number of absentees by its probability and sum these products.

Step 4 ：Let's denote the number of absentees as \(a\) and their corresponding probabilities as \(p\). The numbers of absentees are \(a = [0, 1, 2, 3, 4, 5, 6]\) and the corresponding probabilities are \(p = [0.01, 0.06, 0.11, 0.27, 0.35, 0.13, 0.07]\).

Step 5 ：The expected value is then calculated as \(E = \sum a \times p\).

Step 6 ：By substituting the values of \(a\) and \(p\) into the formula, we get the expected value \(E = 3.56\).

Step 7 ：Final Answer: The expected number of absentees on a given day is \(\boxed{3.56}\).