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Stat 776 Homework 4: Probability Distributions and Independence - Prof. Xiaomi Hu, Assignments of Data Analysis & Statistical Methods
Solutions to problem 4 of a statistics homework. The problems involve finding distributions of random variables and determining if two random variables are independent. The homework is for a statistics course, specifically stat 776.
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Stat 776 HW
- X =
X 1
X 2
X 3
∼ N
− 1
0
,
1 2 − 1
0 − 1 1
(a) Find the distribution of X 3 X 3 ∼ N (1, 1)
(b) Find the distribution of
( X
1 X 2
)
( X
1 X 2
)
∼ N
(( − 1
0
)
,
( 5
))
X 1
X 2
X 3
∼ N
− 3
,
3 − 1 0
− 1 3 0
. Suppose X 1 + X 2 and ( (^) aX 1 −^ X 2 bX 2 + X 3
)
are independent. Find a and b.
(1, 1 , 0)
3 − 1 0
− 1 3 0
a 0 − 1 b 0 1
= (0, 0)
( (^) a b