Let X Be a Continuous Random Variable with a Cumulative $\mathrm { F } ( \mathrm { x } ) = 1 - \mathrm { e } ^ { - \mathrm { x } ^ { 2 } } ( \mathrm { x } \geq 0 )$

question 7

Multiple Choice

Let X be a continuous random variable with a cumulative distribution function $\mathrm { F } ( \mathrm { x } ) = 1 - \mathrm { e } ^ { - \mathrm { x } ^ { 2 } } ( \mathrm { x } \geq 0 )$ . Find $\operatorname { Pr } ( 1 \leq X \leq 2 )$

• A) \(\mathrm { e } ^ { - 1 }\) - \(e ^ { - 4 }\)
• B) \(\mathrm { e } ^ { - 1 }\) - \(e ^ { - 2 }\)
• C) 1 - \(\mathrm { e } ^ { - 1 }\) - \(e ^ { - 2 }\)
• D) \(\mathrm { e } ^ { - 1 }\) - \(e ^ { - 2 }\) - 2
• E) none of these

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Definitions:

Salvage Value

The estimated resale value of an asset at the end of its useful life, considered in depreciation calculations and asset disposal decisions.

Annual Net Cash Flows

The total amount of cash that a company generates or loses over one year, after all expenses and incomes are taken into account.

Depreciated

A reduction in the value of an asset over time, often due to wear and tear or obsolescence, which is accounted for in accounting to spread the cost over its useful life.

Marginal Tax Rate

The marginal tax rate is the rate at which the last dollar of income is taxed, reflecting the rate applied to an individual's or entity's highest level of income.