Consider a discrete random variable $X$ that represents the outcome of a game where a player can win the following amounts based on a fair six-sided die roll: If the player rolls a 1 or 2, they win $10. If the player rolls a 3 or 4, they win $20. If the player rolls a 5, they win $30. If the player rolls a 6, they win nothing. Calculate the expected value $E(X)$ and the variance $ ext{Var}(X)$ of the winnings from this game. Which of the following statements is true?

Exam

CFA Level 1

Section

Difficulty

Quantitative Methods

Expected Value and Variance of Game Winnings

Hard Probability Concepts Expected Value And Variance

Consider a discrete random variable $X$ that represents the outcome of a game where a player can win the following amounts based on a fair six-sided die roll:

If the player rolls a 1 or 2, they win $10.
If the player rolls a 3 or 4, they win $20.
If the player rolls a 5, they win $30.
If the player rolls a 6, they win nothing.

Calculate the expected value $E(X)$ and the variance $ ext{Var}(X)$ of the winnings from this game. Which of the following statements is true?

The expected value $E(X)$ is $15$ and the variance $ ext{Var}(X)$ is $35.$

The expected value $E(X)$ is $14$ and the variance $ ext{Var}(X)$ is $40.$

The expected value $E(X)$ is $16$ and the variance $ ext{Var}(X)$ is $45.$

Hint

Submitted4.9K

Correct3.3K

% Correct67%