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Random variables X1,..., Xn are IID with N(1,0²), Y1,., Yn2 are IID with N(µy,o²), and X;'s and Y;'s are independent. Let's define the following random variables: X1+...+ Xn Y1 + ...+Yn2 E, (X¡ – X)² E, (Yi – Ý)² Ý = %3D n2 nị – 1 n2 – 1 (1) Give the PDF of X.

Random variables X1,..., Xn are IID with N(1,0²), Y1,., Yn2 are IID with N(µy,o²), and X;'s and Y;'s are independent. Let's define the following random variables: X1+...+ Xn Y1 + ...+Yn2 E, (X¡ – X)² E, (Yi – Ý)² Ý = %3D n2 nị – 1 n2 – 1 (1) Give the PDF of X.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. Random variables X1,..., Xnı are IID with N(µr,0²), Y1,.., Yn2 are IID with N(µy,o²), and X;'s and Y;'s are independent. Let's define the following random variables: X1+...+ Xnị Y1 +...+Yn2 E, (X; – X)² n1 – 1 n2 – 1 n2 (1) Give the PDF of X. (2) Find the PDF of (n1 – 1) S2 + (n2 – 1) S.
Transcribed Image Text:5. Random variables X1,..., Xnı are IID with N(µr,0²), Y1,.., Yn2 are IID with N(µy,o²), and X;'s and Y;'s are independent. Let's define the following random variables: X1+...+ Xnị Y1 +...+Yn2 E, (X; – X)² n1 – 1 n2 – 1 n2 (1) Give the PDF of X. (2) Find the PDF of (n1 – 1) S2 + (n2 – 1) S.
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