Question 1

According to the Railway Association of Canada^[i] "collisions at rail crossings and as a result of trespassing on railway property account for more than 85 per cent of all rail-related injuries and deaths in Canada over the last 10 years". As an example, in 2016, 66 people were killed and 44 were seriously injured^[ii].

Operation Lifesaver (OL) is a not-for-profit that is funded by Transport Canada and the Railway Association of Canada. Its mandate is to raise public awareness about the hazards associated with railway tracks and trains.^[iii] Via Rail's Risk Manager has proposed a capital investment that is in keeping with the OL Look. Listen. Live campaign to Via's executive officers for consideration. The concept involves installing decals at all Via Rail railway crossings that are within 100 meters of a subdivision, business district or industrial park district in the Greater/Metro Vancouver

area.

The new decals would cost $15,000 per location or $2,955,000 for all 197 locations and will result in an annual return of $985,000 due to a decrease in liability claims. The decals have no salvage value at the end of their seven (7) year life span. The income tax rate is 40 percent.

The executive officers will want to see all the calculations in responding to the following:

1. Determine whether the decals will have a positive net present value if the minimum acceptable rate of return is 10 percent per year compounded annually? (Factor = 4.868)

1. The Risk Manager had some difficulty in convincing the executive officers of the $985,000 savings which in turn could be viewed as additional annual revenue. If the following probability distribution applied to each year's additional revenue and the executive officers wanted to make its decisions on the basis of the expected value of this additional revenue, should they invest in the decals?

Probability %		Additional Savings/Revenue $
.10		750,000
.35		985,000
.25		1,025,000
.15		1,200,000
.10		1,350,000
.05		1,700,000

^[i] Railway Association of Canada. https://www.railcan.ca/news/canadas-railways-support-new-federal-rail-safety-program

^[ii] Transportation Safety Board of Canada. Canadian crossing and trespassing incident data for 2016.

^[iii]https://www.tc.gc.ca/en/railsafetyactreview/documents/OL_RSA_Review_Submission-11-09-2017.pdf

Question 2

1. Following a statement by Operation Lifesaver^[iii]:

Mapping applications such as Google Maps, Apple's iMaps, Waze and Garmin are ubiquitous nowadays, yet most don't currently include Canadian railway crossing information. The U.S. National Transportation Safety Board recently requested that technology companies include audio and visual alerts of upcoming railway crossings in their mapping applications following a tragic collision between a truck and a commuter train in California.7 OL has made a similar request of Google Canada and would recommend that the federal government encourage inclusion of this information in all mapping applications in Canada. The Railway Association of Canada has collected location data for all crossings as part of its Canadian Rail Atlas project and could make this information available to technology companies for this purpose.

The Railway Association is considering the purchase of sensors to connect to various mapping technologies. The sensors, which could be purchased for $300 each, can be expected to have a useful life of seven years, with no salvage value. If the Railway Association management wishes to earn an annual after tax, time adjusted rate of return of at least 6% on its funds, compute the minimum after-tax cash flow that each sensor would have to generate to attain this rate of return. (For 6%, 7 years, the present value factor is 5.582).

Question 3

Referring to the Confusion Matrix, apply the Predictive Model to Via Rails 2018 in train passenger injury data. In 2018, 4,390,000 passengers travelled on Via Rail trains and 1,600 were injured. How often did the model correctly and incorrectly predict for each passenger "yes, will have an accident" or "no, will not have an accident"?

	Predicted No	+	Predicted Yes	=	Total (4,390,000)
Actual No	4,388,000		400		4,388,400
Actual Yes	620		980		1,600

1. Identify:
   1. the True Positives
   2. the True Negatives
   3. the False Positives
   4. The False Negatives
   5. Calculate the Accuracy
   6. Calculate the Precision
   7. Calculate the Recall

Calculate the F-score