Question

1. 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