The Lifetime X (In Hundreds of Hours) of a Certain $\alpha = 2 \text { and } \beta = 3$

question 4

Essay

The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters $\alpha = 2 \text { and } \beta = 3$ Compute the following:
a. E(X) and V(X)
b. $P ( X \leq 3 )$
c. $P ( 1.5 \leq X \leq 6 )$

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Definitions:

Opportunity Costs

The cost of foregoing the next best alternative when making a decision.

Financing Costs

Expenses a company pays to borrow funds or raise capital through equity, including interest payments, fees, and other charges.

Depreciation Costs

The allocation of the cost of an asset over its useful life, reflecting the decrease in value due to wear and use.

Cost Of Capital

The rate of return that a company must offer investors to finance its assets, often used in making investment decisions.