Question: RMI 2101 Homework Assignment 6 Due Dates On-time Submission Be careful to follow the Guidelines for Homework Document & Directions for Turnitin on Canvas/Home/Course Documents.

RMI 2101

Homework Assignment 6

Due Dates

On-time Submission

Be careful to follow the Guidelines for Homework Document & Directions for Turnitin on Canvas/Home/Course Documents.

Amazon owns trucks used for cargo shipment. In the course of their activities, Amazon sustains losses in the form of property damages to their trucks. Assume that Amazon owns a truck station located in Pennsylvania (PA) and also another station in New Jersey (NJ).

The PA station has 3200 trucks in total, while the NJ station has 4800 trucks in total.

Amazon has the following sample for the reported number of accidents per truck in the PA station and NJ station, respectively.

# of accidents per truck per year	# of trucks of having this # of accidents
# of accidents per truck per year	PA Station	NJ Station
0	2560	3936
1	480	576
2	160	288

a. What is the random variable illustrated here? [1 point]

b. Calculate the expected value of frequency per truck for the PA station and the NJ station, respectively. Show all work. What are the units of measurement? [3 points]

c. Calculated the variance of frequency per truck for the PA station and the NJ station, respectively. Show all work! What are the units of measurement? [3 points]

d. How much risk is present for the PA station and the NJ station, respectively? Round your calculation to 2 decimals. Which truck station is riskier, PA station or NJ station? Show all work. What are the units of measurement? [3 points]

Based on the information in PA station, Amazon has constructed the following table related to the dollar amount of losses for 800 accidents reported in the sample.

$ amount of losses	# of accidents having this $ amount of losses
$300	640
$2000	120
$3200	40

Derive the probability distribution of the dollar amount of losses based on this data. Be careful to label exactly what you are defining as the probability distribution. [2 points]

Calculate the expected value of severity per truck in PA station. Show all work. [1 point]

Calculate the expected loss per truck in PA station. Show all work. [2 points]

Calculate the expected loss for ALL trucks in PA station. Show all work. [1 point]

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