A Crew of Mechanics at the Highway Department Garage Repair

question 57

Essay

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution.
(a) What is the probability that the system is empty?
(b) What is the probability that there is precisely one vehicle in the system?
(c) What is the probability that there are more than two vehicles in the system?
(d) What is the probability of 5 or more vehicles in the system?

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Definitions:

Wash Sale Rules

IRS regulations that disallow the claim of a capital loss for tax purposes if a substantially identical security is purchased within 30 days before or after the sale.

Loss Disallowed

A financial loss that cannot be deducted from taxable income as per tax regulations, often due to specific restrictions or limitations.

Personal Residence

The primary dwelling in which a person lives, often eligible for certain tax benefits, like the deduction of mortgage interest and property taxes.

Gain Recognize

Gain Recognize refers to the process of reporting the profit earned from the sale of an asset for tax purposes.