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ACTUARY EXAM P QUESTIONS & ANSWERS 2023/2024
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ACTUARY EXAM P QUESTIONS & ANSWERS 2023/2024 Continuos Marginal Density of y - ANSWER-integrate over all possible values of x to determine marginal density of y. ∫from(y to 1) (2x+y)dx =2[(ײ÷2) - xy]from(y to 1) =1+2y-3y² Percentiles(discrete, continous) - ANSWER-discrete = 50th %...

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  • October 20, 2023
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  • 2023/2024
  • Exam (elaborations)
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ACTUARY EXAM P QUESTIONS &
ANSWERS 2023/2024

Continuos Marginal Density of y - ANSWER-integrate over all possible values of x to determine marginal
density of y.

∫from(y to 1) (2x+y)dx

=2[(ײ÷2) - xy]from(y to 1)

=1+2y-3y²



Percentiles(discrete, continous) - ANSWER-discrete = 50th % or median is Fx(π₅₀) ≥ .50, or the first
instance in which Fx is greater than .5



continous = 50th % is ∫from(0 to π₅₀)f(x)dx =.5



integrating with exponent on bottom - ANSWER-bring exponent to the top, add one and still divide by
the new ∫²₁(3÷x⁴)dx = ∫²₁3x⁻⁴ = -3/3x³ = -1/x³



differentiating moment generating function - ANSWER-(d/dx)(3/3-x)² = (d/dx)9/(3-x)² = 18/(3-x)³

evaluate at x=0 for E[x]



Integrating exponential distributions - ANSWER-when exponentially distributed and a policy limit of 25k
∫₀²⁵ xe^-x/10k +∫25ke^-x/10k



Moment Generating Functions - ANSWER-Mx(t) = (β/β-t)∧α

E(x) = M'x(0) = αβ∧(α)(α+1)(β-t)^-(a+2)=α/β

E(x²) = α(α+1)/β²



derivative of n/(n-t) = 1/n

3/(3-t) =1/3

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