Question

- The waitress at the local diner estimates that she receives a $4 tip from 20% of tables, $6 tip from 25% of tables, and $5 tip from 50% of tables while 5% of tables leave no tip. What is her expected value of a tip from any given table?

Answer #1

Let X be the random variable which denotes the value of the tip.

Therefore, X can take the values 0, 4, 5, 6.

The probability distribution of X is

X | 0 | 4 | 5 | 6 |

P(X = x) | 0.05 | 0.20 | 0.50 | 0.25 |

The expected value of a tip from any given table is

E(X) = x * P(X = x)

= (0 * 0.05) + (4 * 0.20) + (5 * 0.50) + (6 * 0.25)

= 0 + 0.8 + 2.5 + 1.5

E(X) = 4.8

Therefore, the expected value of a tip from any given table is
**$4.8**

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