This Exam P sample reference tests Pareto-Type Moments. Integrating x times the density gives E[X]=(p-1)/(p-2). Setting this mean to 2 yields p=3, choice C.
The density is a Pareto-type density on values above one. A finite mean requires the parameter to exceed two, and integrating the value times the density gives the displayed mean.
E[X]=(p−1)∫1∞x1−pdx,p>2
Model
Model
Equate the resulting mean expression to the stated value of two.
E[X]=p−2p−1=2
Compute
Compute
Solving the linear equation gives a parameter value of three, which satisfies the required condition for a finite mean.
p−1=2p−4,p=3
Answer
Answer
The density parameter is 3.
3(C)
Continue without hunting through PDFs
All 718 Exam P sample solutions in syllabus order
The searchable 3108-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
