3. The exponential probability distribution is useful in describing the
time it takes to complete a task.
The exponential random variables can be used to describe:
Time between vehicle arrivals at a toll booth
Time required to complete a questionnaire
Distance between major defects in a highway
The time between goals scored in a World Cup
soccer match
4. f x e x
( ) /
1
for x > 0, > 0
Density Function
where: = mean
e = 2.71828
6. Example: Al’s Full-Service Pump
The time between arrivals of cars at Al’s full-service gas pump follows
an exponential probability distribution with a mean time between
arrivals 3 minutes. Al would like to know the probability that the time
between two successive arrivals will be 2 minutes or less.
P(x < 2) = 1 - 2.71828-2/3 = 1 - .5134 = .4866
Solution:
7. Example:
If jobs arrive every 15 seconds on average, λ = 4 per minute,
what is the probability of waiting less than or equal to 30
seconds, i.e .5 min? P(T ≤ .5).
8. Characteristics :
The mean and standard deviation of exponential distribution are equal.
The distribution is extremely skewed and there does not exist any mode.