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(Created page with "'''Solution: E''' <math display = "block"> F ( y ) = Pr [Y ≤ y ] = Pr [10 X 0.8 ≤ y] = Pr[ X \leq (Y/10)^{10/8}] = 1-\exp(-(Y/10)^{10/8}). </math> Therefore, <math dis...") |
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<math display = "block"> | <math display = "block"> | ||
F ( y ) = | F ( y ) = \operatorname{P}[Y ≤ y ] = \operatorname{P}[10 X 0.8 ≤ y] = \operatorname{P}[ X \leq (Y/10)^{10/8}] = 1-\exp(-(Y/10)^{10/8}). | ||
</math> | </math> | ||
Latest revision as of 18:51, 4 May 2023
Solution: E
[[math]]
F ( y ) = \operatorname{P}[Y ≤ y ] = \operatorname{P}[10 X 0.8 ≤ y] = \operatorname{P}[ X \leq (Y/10)^{10/8}] = 1-\exp(-(Y/10)^{10/8}).
[[/math]]
Therefore,
[[math]]
f(y) = F^{'}(y) = \frac{1}{8} \left ( \frac{Y}{10}\right )^{1/4} \exp(-(Y/10)^{5/4}).
[[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.