SOLUTION: Suppose the joint probability density function of (X, Y) is given by F(x,y)=(2x+y)/210, 2≤x≤6;0≤y≤5 = 0, otherwise Show that ∫

SOLUTION: Suppose the joint probability density function of (X, Y) is given by F(x,y)=(2x+y)/210, 2≤x≤6;0≤y≤5 = 0, otherwise Show that ∫_(-∞

Question 1086742: Suppose the joint probability density function of (X, Y) is given by
F(x,y)=(2x+y)/210, 2≤x≤6;0≤y≤5
= 0, otherwise
Show that
∫_(-∞)^∞▒∫_(-∞)^∞▒〖f(x,y)dxdy=1〗
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Since the function equals zero outside the rectangle, we can reduce the limits of integration to,

Evaluating,

So,

Evaluating,

.
.
.

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SOLUTION: Suppose the joint probability density function of (X, Y) is given by F(x,y)=(2x+y)/210, 2&#8804;x&#8804;6;0&#8804;y&#8804;5 = 0, otherwise Show that &#8747;_(-&#8734;

SOLUTION: Suppose the joint probability density function of (X, Y) is given by F(x,y)=(2x+y)/210, 2≤x≤6;0≤y≤5 = 0, otherwise Show that ∫_(-∞