Let Z1, Z2 be a random sample of size 2 from N(0, 1), and X1, X2 a random sample of size 2 from N(1, 1). Suppose the Z;'s are independent of the X;'s. Q4.1 What is the distribution of X + Z? Q4.2 What is the distribution of (Zı + Z2)/ V[(X2 – X1)² + (Z2 – Z1)²]/2? | Q4.3 What is the distribution of [(X1 – X2)? + (Z1 – Z2)² + (Z1 + Z2)*]/2? -

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let Z1, Z2 be a random sample of size 2 from N(0, 1), and X1, X2 a random sample of size 2
from N(1, 1). Suppose the Z;'s are independent of the X;'s.
Q4.1
What is the distribution of X + Z?
Q4.2
What is the distribution of
(Z1 + Z2)/ V[(X2 – X1)² + (Z2 – Z1)²]/2?
Q4.3
What is the distribution of
[(X1 – X2)² + (Z1 – Z2)² + (Z1 + Z2)²]/2?
-
Q4.4
!
What is the distribution of (X2 + X1 – 2)²/(X2 – X1)?
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Transcribed Image Text:Let Z1, Z2 be a random sample of size 2 from N(0, 1), and X1, X2 a random sample of size 2 from N(1, 1). Suppose the Z;'s are independent of the X;'s. Q4.1 What is the distribution of X + Z? Q4.2 What is the distribution of (Z1 + Z2)/ V[(X2 – X1)² + (Z2 – Z1)²]/2? Q4.3 What is the distribution of [(X1 – X2)² + (Z1 – Z2)² + (Z1 + Z2)²]/2? - Q4.4 ! What is the distribution of (X2 + X1 – 2)²/(X2 – X1)? -
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