Math Problem Statement
Suppose 𝑋𝑖∼Normal(0,1𝑖2)Xi∼Normal(0,i21), where 𝑖=1,2,…,9i=1,2,…,9 and 𝑋1,𝑋2,…,𝑋9X1,X2,…,X9 are independent to each other. Let 𝑌Y be a random variable defined as 𝑌=∑𝑖=19𝑖𝑋𝑖Y=i=1∑9iXi. Find the variance of 𝑌Y
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Random Variables
Normal Distribution
Formulas
Variance of a linear combination of random variables
Theorems
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Suitable Grade Level
Advanced Undergraduate
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