4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the mean and variance of Y?
4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the mean and variance of Y?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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Question
Let X1 ∼ N(μ = 2, σ^2 = 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the mean and variance of Y?
Expert Solution
Step 1
A random variable follows a Normal distribution with mean and variance
Random Variable | Mean | Variance |
X1 | 2 | 4 |
X2 | 1 | 16 |
X3 | -4 | 9 |
The random variables X1, X2 and X3 are independent
Given Y is another random variable
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