Question

Find the expected value from the expected value table.

Short answer

Expected value is$5.4.$

Step-by-step solution

Given Information

Sam participates in community events as a volunteer. In a month, he performs no more than five events. He attends exactly five activities $35\%$of the time, four events $25\%$of the time, three events $20\%$of the time, two events $10\%$of the time, one event $5\%$of the time, and no events $5\%$of the time.

Explanation

According to the data in the table above, the expected value of the random variable is the sum of the entries in the column $x^{*}\mathbf{P}\left(\mathrm{x}\right)$that is

$2(0.1)+\left(4\right(0.3)+6(0.4)+8(0.2)=0.2+1.2+2.4+1.6=5.4$

As a result, the expected value is$5.4.$