The Amazon. com, Inc. 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 the Amazon owns a truck station located in Pennsylvania (PA) and also another station in New Jersey (NJ). The PA station has 3,000 trucks in total, while the NJ station has 1,200 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
PA Station NJ Station
0 117 264
1 24 32
2 9 24

Required:
a. What is the random variable illustrated here?
b. Calculate the expected value of frequency per truck in PA station and NJ station, respectively. What are the units of measurement?
c. Calculated the variance of frequency per truck in the PA station and the NJ station, respectively. What are the units of measurement?
d. How much risk is present in the PA station and the NJ station, respectively?Which truck station is riskier, the PA station or the NJ station?What are the units of measurement?

Kindly check explanation

Explanation:

Given the data:

# of accidents per truck per year # of trucks of having this # of accidents

f(X) PA Station NJ Station

0 117 264

1 24 32

2 9 24

a. What is the random variable illustrated here?

Number of accident per truck per year

b. Calculate the expected value of frequency

per truck in PA station and NJ station, respectively.

Expected value of frequency per truck in PA Station :

Σ(accident per truck * # truck having the accident)

E(x) = Σ(0*117) + (1 * 24) + (2 * 9) = 42

Expected value of frequency per truck in NJ Station :

Σ(accident per truck * # truck having the accident)

E(x) = Σ(0*264) + (1 * 32) + (2 * 24) = 80

c.) Calculated the variance of frequency per truck in the PA station and the NJ station, respectively.

The variance (V) :

Σ(X²*f(x)) - E(x)²

NJ Station :

(0 * 264^2) + (1 * 32^2) + (2 * 24^2) - 42^2

(0 + 1024 + 1152) - 1764

= 412

PA Station:

Σ(0*117^2) + (1 * 24^2) + (2 * 9^2) - 80^2

= (0 + 576 + 162) - 6400

= - 5562

d. PA Station is riskier

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explanation:

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