Expectation and variance of discrete random variables Quiz

1. $X$ takes values 1, 2, 3 with probabilities 0.5, 0.3, 0.2. Find $E(X)$.

• A. $2$
• B. $1.7$
• C. $0.6$
• D. $2.3$

2. $E(X)=4$ and $E(X^2)=19$. Find $\mathrm{Var}(X)$.

• A. $3$
• B. $15$
• C. $35$
• D. $9$

3. $E(X)=5$ and $\mathrm{Var}(X)=2$. Find $E(4X-1)$.

• A. $19$
• B. $7$
• C. $9$
• D. $21$

4. $\mathrm{Var}(X)=2$. Find $\mathrm{Var}(5-3X)$.

• A. $-1$
• B. $-6$
• C. $13$
• D. $18$

5. A game costs 3 pounds to play and has expected prize 2.5 pounds. What is the expected net gain?

• A. $0.5$ pounds
• B. $5.5$ pounds
• C. $-0.5$ pounds
• D. $-7.5$ pounds