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?

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Definitions:

McClelland's Model

A psychological theory of motivation that asserts people are motivated by three primary needs: achievement, affiliation, and power.

Personal Relationships

Interpersonal connections formed between individuals based on shared interests, emotions, and other social commitments.

Esteem Needs

A higher-level requirement in Maslow's hierarchy of needs that includes the desire for respect, status, recognition, and self-esteem.

Maslow's Hierarchy

A theory in psychology proposing that people are motivated by five basic categories of needs: physiological, safety, love/belonging, esteem, and self-actualization, prioritized hierarchically.