Question

The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution:

Time Between Emergency Calls (hours)	Probability
1	0.05
2	0.10
3	0.30
4	0.30
5	0.20
6	0.05
	1.00

The squad is on duty 24 hours per day, 7 days per week.

b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probabilistic distribution. Why are the results different?

Answer 1

Solution:

Average time b/w calls = (1+2+3+4+5+6)/6 = 21/6 = 3.5

Expected value of the time b/w calls from probability distribution =(1×0.05)+(2×0.1)+(3×0.3)+(4×0.3)+(5×0.2)+(6×0.05) =0.05+0.2+0.9+1.2+1+0.3= 3.65

Because mean is used for frequency distribution while expected mean used for probability distribution .

Expected value is the long run average value of repetition of the experiments it represents.

Expected value calculated on relative frequency while mean calculates on frequency.