Question

Problem 1. Let's play with some math derivations. Let Y = (Y1, Y2)' be independent random variables with expected values ? = (?1, ?2)'. Also we know that the variance covariance matrix for Y is ? = ( ?1^2 0 ; 0 ?2^2 ). Suppose a = (a1, a2)' is a vector of constants, please a. show that E(a' Y) = a' ?. b. show that V (a'Y) = a' ?a.

          Problem 1. Let's play with some math derivations.

Let Y = (Y1, Y2)' be independent random variables with expected values ? = (?1, ?2)'. Also we know that the variance covariance matrix for Y is
? = ( ?1^2 0 ; 0 ?2^2 ). Suppose a = (a1, a2)' is a vector of constants, please

a. show that E(a' Y) = a' ?.

b. show that V (a'Y) = a' ?a.

Problem 1. Let's play with some math derivations.

Let Y = (Y1, Y2)' be independent random variables with expected values ? = (?1, ?2)'. Also we know that the variance covariance matrix for Y is
? = ( ?1^2 0 ; 0 ?2^2 ). Suppose a = (a1, a2)' is a vector of constants, please

a. show that E(a' Y) = a' ?.

b. show that V (a'Y) = a' ?a.

Added by Christy O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/15/2023

Step 1

First, we need to find the expected value of a'Y. Recall that the expected value of a random variable is the sum of the product of each possible value and its probability. Since Y is a vector of random variables, we can write the expected value as follows: E(a'Y) Show more…

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Problem 1. Let's play with some math derivations. Let Y = (Y1, Y2)' be independent random variables with expected values μ = (μ1, μ2)'. Also we know that the variance covariance matrix for Y is Σ = ( σ1^2 0 ; 0 σ2^2 ). Suppose a = (a1, a2)' is a vector of constants, please a. show that E(a' Y) = a' μ. b. show that V (a'Y) = a' Σa.