Prove that for any constant k, extVar(kX + Y) = k2 extVar(X) + extVar(Y) given X and Y are two independent random variables.

April 26, 2026Mathematics

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April 26, 2026

Answer

E(Z^2) - (E(Z))^2$.

Hey belackırine@gmail.com, good to see you again.

Here's the solution to question 3:

Part (i): Prove that for any constant $k$ , $\text{Var}(kX + Y) = k^2Var(X) + Var(Y)$ given $X$ and $Y$ are two independent random variables.

Step 1: Use the definition of variance, $\text{Var}(Z) = E(Z^2) - (E(Z))^2$ . Let $Z = kX + Y$ .

Step 2: Calculate $E(Z)$ . Since expectation is linear:

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Hey belackırine@gmail.com, good to see you again. Here's the solution to question 3: Part (i): Prove that for any constant k, Var(kX + Y) = k^2Var(X) + Var(Y) given X and Y are two independent random variables.

Asked on April 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 26, 2026

Hey belackırine@gmail.com, good to see you again. Here's the solution to question 3: Part (i): Prove that for any constant k, Var(kX + Y) = k^2Var(X) + Var(Y) given X and Y are two independent random variables. Step 1: Use the definition of variance, Var(Z) = E(Z^2) - (E(Z))^2. Let Z = kX + Y. Step 2: Calculate E(Z). Since expectation is linear: E(kX + Y) = E(kX) + E(