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Asked Sep 14, 2019
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Please, help me with very detailed and self-explanatory solutions. thank you

Exercise 1. Answer the following
(a) If, px,y (i,) =
- 2^^j /j!,0 < i < j, find the pmf for X and Y
е
(b) Given
1 +x
-1 x< 0,
f(x)
< 1
1 — х, 0<х
otherwise
Find E(X2)andVar(X2
(c) If f(x, y) 2, 0 <y
1, Find Cov(X, Y) and marginal pdf of X
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Exercise 1. Answer the following (a) If, px,y (i,) = - 2^^j /j!,0 < i < j, find the pmf for X and Y е (b) Given 1 +x -1 x< 0, f(x) < 1 1 — х, 0<х otherwise Find E(X2)andVar(X2 (c) If f(x, y) 2, 0 <y 1, Find Cov(X, Y) and marginal pdf of X

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Expert Answer

Step 1

To determine the required probability mass functions 

Step 2

(a) pmfs of X and Y are obtained by summing over the Y and X values respectively

(a)Pr()=e
i=0,1..
i
PyG)=
j!
j= 0,1,..
i
i=0
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(a)Pr()=e i=0,1.. i PyG)= j! j= 0,1,.. i i=0

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Step 3

(b)

...
0
1
(b)E(X)=x (1+x)dx + [x* (1- x)ch
0
1
6
Var(X2) ECY)E(x2
0
1
=x(+x)d+x(1-x)cdx-
36
1
1
1
30 36 180
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0 1 (b)E(X)=x (1+x)dx + [x* (1- x)ch 0 1 6 Var(X2) ECY)E(x2 0 1 =x(+x)d+x(1-x)cdx- 36 1 1 1 30 36 180

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