Find distribution functions of combination of two random variables
$begingroup$
$ξ$ and $η$ are independent random variables with distribution functions $F(x)$ and $G(x)$ correspondingly.
How do you find the distribution functions of random variables listed below in terms of a combination of $F(x)$ and $G(x)$?
$ζ_1=max(xi,eta)$
$ζ_2=min(xi,eta)$
$ζ_3=max(ξ,2η)$
random
edited Jan 8 at 14:13
amWhy
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
$endgroup$
add a comment |
$begingroup$
$ξ$ and $η$ are independent random variables with distribution functions $F(x)$ and $G(x)$ correspondingly.
How do you find the distribution functions of random variables listed below in terms of a combination of $F(x)$ and $G(x)$?
$ζ_1=max(xi,eta)$
$ζ_2=min(xi,eta)$
$ζ_3=max(ξ,2η)$
random
edited Jan 8 at 14:13
amWhy
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
$endgroup$
$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51
add a comment |
$begingroup$
$ξ$ and $η$ are independent random variables with distribution functions $F(x)$ and $G(x)$ correspondingly.
How do you find the distribution functions of random variables listed below in terms of a combination of $F(x)$ and $G(x)$?
$ζ_1=max(xi,eta)$
$ζ_2=min(xi,eta)$
$ζ_3=max(ξ,2η)$
random
edited Jan 8 at 14:13
amWhy
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
$endgroup$
$ξ$ and $η$ are independent random variables with distribution functions $F(x)$ and $G(x)$ correspondingly.
How do you find the distribution functions of random variables listed below in terms of a combination of $F(x)$ and $G(x)$?
$ζ_1=max(xi,eta)$
$ζ_2=min(xi,eta)$
$ζ_3=max(ξ,2η)$
random
random
edited Jan 8 at 14:13
amWhy
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
edited Jan 8 at 14:13
amWhy
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
edited Jan 8 at 14:13
amWhy
1
edited Jan 8 at 14:13
amWhy
1
edited Jan 8 at 14:13
amWhy
1
1
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
asked Oct 30 '17 at 13:10
mark.keanemark.keane
476
476
$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51
add a comment |
$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51
$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Figured it out right after drhab hint.
$zeta_1 = $ $P(zeta_1≤x)$ = $P(zeta≤x land eta ≤x)$ = $F(x)G(x)$
$zeta_2 = $ $P(zeta_2≤x)$ = $P(zeta≤x lor eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$zeta_3 = $ $P(zeta_3≤x)$ = $P(zeta≤x land 2eta ≤x)$ = $F(x)G(frac{x}{2})$.
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Figured it out right after drhab hint.
$zeta_1 = $ $P(zeta_1≤x)$ = $P(zeta≤x land eta ≤x)$ = $F(x)G(x)$
$zeta_2 = $ $P(zeta_2≤x)$ = $P(zeta≤x lor eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$zeta_3 = $ $P(zeta_3≤x)$ = $P(zeta≤x land 2eta ≤x)$ = $F(x)G(frac{x}{2})$.
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
$endgroup$
add a comment |
$begingroup$
Figured it out right after drhab hint.
$zeta_1 = $ $P(zeta_1≤x)$ = $P(zeta≤x land eta ≤x)$ = $F(x)G(x)$
$zeta_2 = $ $P(zeta_2≤x)$ = $P(zeta≤x lor eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$zeta_3 = $ $P(zeta_3≤x)$ = $P(zeta≤x land 2eta ≤x)$ = $F(x)G(frac{x}{2})$.
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
$endgroup$
add a comment |
$begingroup$
Figured it out right after drhab hint.
$zeta_1 = $ $P(zeta_1≤x)$ = $P(zeta≤x land eta ≤x)$ = $F(x)G(x)$
$zeta_2 = $ $P(zeta_2≤x)$ = $P(zeta≤x lor eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$zeta_3 = $ $P(zeta_3≤x)$ = $P(zeta≤x land 2eta ≤x)$ = $F(x)G(frac{x}{2})$.
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
$endgroup$
Figured it out right after drhab hint.
$zeta_1 = $ $P(zeta_1≤x)$ = $P(zeta≤x land eta ≤x)$ = $F(x)G(x)$
$zeta_2 = $ $P(zeta_2≤x)$ = $P(zeta≤x lor eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$zeta_3 = $ $P(zeta_3≤x)$ = $P(zeta≤x land 2eta ≤x)$ = $F(x)G(frac{x}{2})$.
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
answered Oct 30 '17 at 15:11
mark.keanemark.keane
476
476
add a comment |
add a comment |
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$begingroup$
Do you agree that $mathsf P(zeta_1leq x)=mathsf P(xileq xwedgeetaleq x)$?
$endgroup$
– drhab
Oct 30 '17 at 13:24
$begingroup$
Yep. Finally solved it in a minute after your hint. Thank you.
$endgroup$
– mark.keane
Oct 30 '17 at 14:51