Sums of independent random variables

Sums of independent random variables Quiz

Spec SD8 · AQA A-Level Further Maths: Quiz

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1. $X$ and $Y$ are independent, $E(X)=4$ , $E(Y)=6$ . Find $E(X+Y)$ .
- A. $10$
- B. $2$
- C. $24$
- D. $5$
2. $X$ and $Y$ are independent, $\text{Var}(X)=2$ , $\text{Var}(Y)=7$ . Find $\text{Var}(X+Y)$ .
- A. $5$
- B. $14$
- C. $9$
- D. $3$
3. Independent $X$ and $Y$ have standard deviations 6 and 8. What is the standard deviation of $X+Y$ ?
- A. $14$
- B. $10$
- C. $100$
- D. $2$
4. Which condition is needed for $\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$ ?
- A. $E(X)=E(Y)$
- B. $X$ and $Y$ are independent
- C. $X$ and $Y$ are both continuous
- D. $\text{Var}(X)=\text{Var}(Y)$
5. $X_1$ and $X_2$ are independent observations of $X$ with $\text{Var}(X)=5$ . Find $\text{Var}(X_1+X_2)$ .
- A. $20$
- B. $25$
- C. $5$
- D. $10$