Consider the following properties of independent normally distributed random variables X and Y (1) E(bX + dY) = bE(X)+ dE(Y), where b and d are constants. (2) var(bX + dY) = b’var(X) + d²var(Y), where b and c are constants AND X and Y are independent. (3) var(X) = E(X²) – [E(X)]² Use these properties (or a generalization of these properties) to show the following. 1. E(C) = ECihi 2. var(C) = -1
Consider the following properties of independent normally distributed random variables X and Y (1) E(bX + dY) = bE(X)+ dE(Y), where b and d are constants. (2) var(bX + dY) = b’var(X) + d²var(Y), where b and c are constants AND X and Y are independent. (3) var(X) = E(X²) – [E(X)]² Use these properties (or a generalization of these properties) to show the following. 1. E(C) = ECihi 2. var(C) = -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the following properties of independent normally distributed random variables X andY.
(1) E(bX + dY) = bE(X)+ dE(Y), where b and d are constants.
b'var(X) + d var(Y), where b and c are constants AND X and Y are
(2) var(bX + dY)
independent.
(3) var(X) = E(X²) – [E(X)]²
Use these properties (or a generalization of these properties) to show the following.
1. E(C) = E1 Cifli
-D1
2. var(C) = -G
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f133c63-1716-41d7-8ec5-0f87428512d1%2F9aeda844-3e96-415a-a6fe-ca9b26b8fe38%2F7rvw3zd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following properties of independent normally distributed random variables X andY.
(1) E(bX + dY) = bE(X)+ dE(Y), where b and d are constants.
b'var(X) + d var(Y), where b and c are constants AND X and Y are
(2) var(bX + dY)
independent.
(3) var(X) = E(X²) – [E(X)]²
Use these properties (or a generalization of these properties) to show the following.
1. E(C) = E1 Cifli
-D1
2. var(C) = -G
%3D
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