Let X and Y be continuous random variables that are uniformly distributed on the region defined by x20, y20, and x+4y≤20. In other words, there is a constant & such that the joint PDF is given by f(x,y)=k for points within this region, and the joint PDF is equal to 0 outside of this region. Find E[X] and E[Y]. Select two answers on this problem. fx (x)= = £fx (x)= 1 1 10 200 1 1 == fx (x): fr (y) 10 10 | £r (v)=²-23 » (y): y 5 25 1 ƒ (») = ²/3 - 12/²³ fr y 5 25 22 »)=²-3x 5 5 x 1 1 20 400 y x ·x

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Let X and Y be continuous random variables that are uniformly distributed on the region defined by
x20, 120, and x+4y≤20. In other words, there is a constant & such that the joint PDF is given by
f(x,y)=k for points within this region, and the joint PDF is equal to 0 outside of this region. Find
E[X] and E[Y]. Select two answers on this problem.
fx (x)=
=
£x (x)=
fr (y):
fr (y)
fr (y)
==
=
=
fx (x):
1 1
10 200
1
10 10
1
1
5 25
5
2
1
25
22
5 5
y
x
y
1 1
20 400
y
x
·x
Transcribed Image Text:Let X and Y be continuous random variables that are uniformly distributed on the region defined by x20, 120, and x+4y≤20. In other words, there is a constant & such that the joint PDF is given by f(x,y)=k for points within this region, and the joint PDF is equal to 0 outside of this region. Find E[X] and E[Y]. Select two answers on this problem. fx (x)= = £x (x)= fr (y): fr (y) fr (y) == = = fx (x): 1 1 10 200 1 10 10 1 1 5 25 5 2 1 25 22 5 5 y x y 1 1 20 400 y x ·x
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