A piece of flat land is in the form of a right triangle with a southern boundary two miles long and eastern boundary one
Posted: Fri Nov 26, 2021 8:32 am
A piece of flat land is in the form of a right triangle with a
southern boundary two miles long and eastern boundary one mile
long. The point at which an airborne seed lands is of interest. The
following assumption will be made: Given that the seed lands within
the boundaries, its coordinates X and Y are
“uniformly” distributed over the surface of the triangle. In other
words, the pair X,Y has a constant joint PDF
fX,Y(x,y) = c>0
for points within the boundaries, and zero
otherwise.
Derive the value of c that makes this a valid joint
PDF?
Derive the marginal PDF of X.
Derive the marginal PDF of Y.
Derive the conditional PDF of Y given X=x.
Derive P(0.1 ≤ Y≤ 0.7| X=0.5)
N y 1-1 х 0 N
southern boundary two miles long and eastern boundary one mile
long. The point at which an airborne seed lands is of interest. The
following assumption will be made: Given that the seed lands within
the boundaries, its coordinates X and Y are
“uniformly” distributed over the surface of the triangle. In other
words, the pair X,Y has a constant joint PDF
fX,Y(x,y) = c>0
for points within the boundaries, and zero
otherwise.
Derive the value of c that makes this a valid joint
PDF?
Derive the marginal PDF of X.
Derive the marginal PDF of Y.
Derive the conditional PDF of Y given X=x.
Derive P(0.1 ≤ Y≤ 0.7| X=0.5)
- A Piece Of Flat Land Is In The Form Of A Right Triangle With A Southern Boundary Two Miles Long And Eastern Boundary One 1 (3.43 KiB) Viewed 102 times