exercise:B28802f29d: Difference between revisions
From Stochiki
(Created page with "Two loss variables <math>L_1</math> and <math>L_2</math> have a strictly increasing continuous joint cumulative distribution <math>F(x,y)</math>. Which of the following expres...") |
No edit summary |
||
| Line 1: | Line 1: | ||
Two loss variables <math>L_1</math> and <math>L_2</math> have a strictly increasing continuous joint cumulative distribution <math>F(x,y)</math>. Which of the following expressions represent the probability that both losses exceed their 95<sup>th</sup> percentile? | Two loss variables <math>L_1</math> and <math>L_2</math> have a strictly increasing continuous joint cumulative distribution <math>F(x,y)</math>. Which of the following expressions represent the probability that both losses exceed their 95<sup>th</sup> percentile? | ||
< | <ul class="mw-excansopts"> | ||
<li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95))</math> with <math>F_X(x) = F(x,\infty)</math> and <math>F_Y(y) = F(\infty, y)</math></li> | <li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95))</math> with <math>F_X(x) = F(x,\infty)</math> and <math>F_Y(y) = F(\infty, y)</math></li> | ||
<li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.</math> with <math>F_X(x) = F(x,\infty)</math> and <math>F_Y(y) = F(\infty, y)</math></li> | <li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.</math> with <math>F_X(x) = F(x,\infty)</math> and <math>F_Y(y) = F(\infty, y)</math></li> | ||
| Line 7: | Line 7: | ||
<li><math>0.05^2</math></li> | <li><math>0.05^2</math></li> | ||
<li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.</math> with <math>F_X(x) = F(\infty, x)</math> and <math>F_Y(y) = F(y, \infty)</math></li> | <li><math>F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.</math> with <math>F_X(x) = F(\infty, x)</math> and <math>F_Y(y) = F(y, \infty)</math></li> | ||
</ | </ul> | ||
Latest revision as of 13:09, 18 March 2024
Two loss variables [math]L_1[/math] and [math]L_2[/math] have a strictly increasing continuous joint cumulative distribution [math]F(x,y)[/math]. Which of the following expressions represent the probability that both losses exceed their 95th percentile?
- [math]F(F_X^{-1}(0.95), F_Y^{-1}(0.95))[/math] with [math]F_X(x) = F(x,\infty)[/math] and [math]F_Y(y) = F(\infty, y)[/math]
- [math]F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.[/math] with [math]F_X(x) = F(x,\infty)[/math] and [math]F_Y(y) = F(\infty, y)[/math]
- [math]F(F_X(0.95), F_Y(0.95)) - 0.9.[/math] with [math]F_X(x) = F(x,\infty)[/math] and [math]F_Y(y) = F(\infty, y)[/math]
- [math]0.05^2[/math]
- [math]F(F_X^{-1}(0.95), F_Y^{-1}(0.95)) - 0.9.[/math] with [math]F_X(x) = F(\infty, x)[/math] and [math]F_Y(y) = F(y, \infty)[/math]