4.7 Discrete random variables and expected value Quiz

1. $X$ takes values 1, 2, 3 with probabilities $0.2$, $0.5$ and $k$. Find $k$.

• A. $0.2$
• B. $0.3$
• C. $0.7$
• D. $0.5$

2. For $x=1,2,3$ with probabilities $0.2$, $0.5$, $0.3$, find $\mathrm{E}(X)$.

• A. $2.0$
• B. $6.0$
• C. $2.1$
• D. $1.0$

3. A player pays 3 AED to play. They win 10 AED with probability $0.2$ and nothing otherwise. Find the expected gain.

• A. $-1$ AED
• B. $+1$ AED
• C. $-3$ AED
• D. $+2$ AED

4. $P(X=x)=\frac{x}{10}$ for $x=1,2,3,4$. Find $\mathrm{E}(X)$.

• A. $2.5$
• B. $0.3$
• C. $10$
• D. $3$

5. $X$ is a player's gain in a game and $\mathrm{E}(X)=0$. This means the game is

• A. won by the player every time
• B. fair
• C. always lost by the player
• D. profitable for the organiser