Joint distribution but not bivariate normal
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Let φ(x,y|ρ) denote the joint density of N2(0; 0; 1; 1; ρ) evaluated at (x,y). Fix ρ =/= ρ' C(−1,1) and define f(x,y) = αφ(x,y|ρ) + (1− α)φ(x,y|ρ'), where αC(0,1). Show that (i) f is a joint pdf, (ii) the marginals fX and fY are both N(0,1).below is the question in image
density-function
asked 12 hours ago
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up vote
0
down vote
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Let φ(x,y|ρ) denote the joint density of N2(0; 0; 1; 1; ρ) evaluated at (x,y). Fix ρ =/= ρ' C(−1,1) and define f(x,y) = αφ(x,y|ρ) + (1− α)φ(x,y|ρ'), where αC(0,1). Show that (i) f is a joint pdf, (ii) the marginals fX and fY are both N(0,1).below is the question in image
density-function
asked 12 hours ago
Flowinfo toall
43
You are supposed to show your work.
– StubbornAtom
12 hours ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let φ(x,y|ρ) denote the joint density of N2(0; 0; 1; 1; ρ) evaluated at (x,y). Fix ρ =/= ρ' C(−1,1) and define f(x,y) = αφ(x,y|ρ) + (1− α)φ(x,y|ρ'), where αC(0,1). Show that (i) f is a joint pdf, (ii) the marginals fX and fY are both N(0,1).below is the question in image
density-function
asked 12 hours ago
Flowinfo toall
43
Let φ(x,y|ρ) denote the joint density of N2(0; 0; 1; 1; ρ) evaluated at (x,y). Fix ρ =/= ρ' C(−1,1) and define f(x,y) = αφ(x,y|ρ) + (1− α)φ(x,y|ρ'), where αC(0,1). Show that (i) f is a joint pdf, (ii) the marginals fX and fY are both N(0,1).below is the question in image
density-function
density-function
asked 12 hours ago
Flowinfo toall
43
asked 12 hours ago
Flowinfo toall
43
asked 12 hours ago
Flowinfo toall
43
asked 12 hours ago
Flowinfo toall
43
asked 12 hours ago
Flowinfo toall
43
43
You are supposed to show your work.
– StubbornAtom
12 hours ago
add a comment |
You are supposed to show your work.
– StubbornAtom
12 hours ago
You are supposed to show your work.
– StubbornAtom
12 hours ago
You are supposed to show your work.
– StubbornAtom
12 hours ago
add a comment |
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You are supposed to show your work.
– StubbornAtom
12 hours ago