Two Components of a Minicomputer Have the Following Joint Pdf $f ( x , y ) = \left\{ \begin{array} { l l } x e ^ { - x ( 1 + y ) } & x \geq 0 \text { and } y \geq 0 \\0 & \text { otherwise }\end{array} \right.$

question 5

Essay

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: $f ( x , y ) = \left\{ \begin{array} { l l } x e ^ { - x ( 1 + y ) } & x \geq 0 \text { and } y \geq 0 \\0 & \text { otherwise }\end{array} \right.$
a. What is the probability that the lifetime X of the first component exceeds 3?
b. What are the marginal pdf"s of X and Y? Are the two lifetimes independent? Explain.
c. What is the probability that the lifetime of at least one component exceeds 3?

Understand the relationship between product lifespan, operating costs, and pricing decisions.

Understand the key economic forces impacting human resource planning.

Know the definitions and purposes of key HRIS and human resource planning terminologies.

Identify human resource surplus and shortage scenarios and their implications.

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Definitions:

Bromated Hydrocarbons

Organic compounds that contain the element bromine bonded to carbon, used in various industrial applications but are often concerning for environmental and health impacts.

Genetic Resistance

The ability of an organism to withstand or be less affected by diseases, pests, or environmental conditions due to its genetic makeup.

Toxicity

The degree to which a chemical substance or a particular mixture of substances can cause harm to an organism or the environment.

Persistence

refers to the enduring existence or continual occurrence of a characteristic, condition, or effect over a long period.