1. The intersection outside my neighborhood is rather congested and hectic. In fact the number of accidents is exponentially distributed with 2 accidents daily on the weekdays, and 7 accidents daily on the weekends. Being the nerd I am, I decided to figure out the following:

The probability an accident will occur within 1 day during the week:

The probability an accident will occur within 1 day during the weekend:

The expected time (in days) between accidents during the week:

The expected time (in days) between accidents during the weekend:

2. Due to this intersection being too hectic, I decided to move out to the country. Now the intersection outside my neighborhood has an astoundingly low number of accidents (according to city data) of only 3 occurring every 10 years (an amazing 0.3 accidents yearly)! I plan to retire here and want to know the probabilities of a few events happening over the next 30 years.

P(number of accidents = 10):

This involves a Poisson probability:

P(number of accidents 5):

P(8 number of accidents 12):

3. I decide to figure out why so many accidents happened at my old intersection. I want to conduct a reliability analysis for a certain component in the stop light at the intersection. Based on prior testing with a similar product, the city believes the Weibull failure-time distribution, with parameter lambda=.400 per day, applies. But you have no basis for establishing beta. Compute at a time span of 5 days (1) the failure rate and (2) the survival probability assuming the following:

Beta = 0.7:

Failure Rate:

Survival Rate:

Beta = 1.8:

Failure Rate:

Survival Rate:

4. Upon further discovery, the component consists of a series system of components designed exactly the same as figure 6-14 in your book (go figure). Suppose each component has a Weibull failure time distribution with beta = 0.5 and lamda = 0.2 per day. Find the system reliability for each of the following spans of time:

t = 30 days:

There are three main sections of the system that I will call A, B, and C

For A:

For B:

For C:

For Total system: (0.237295)(0.086338)(0.165222) = 0.003385