The discrete uniform distribution Quiz

1. $X$ is uniform on $\{1,\ldots,20\}$. Find $\mathrm{P}(X\le5)$.

• A. $\frac1{20}$
• B. $\frac15$
• C. $\frac14$
• D. $\frac13$

2. Find $\mathrm{E}(X)$ for the uniform distribution on $\{1,\ldots,11\}$.

• A. $5.5$
• B. $6$
• C. $11$
• D. $5$

3. Find $\mathrm{Var}(X)$ for a fair six-sided die.

• A. $\frac{35}{12}$
• B. $3$
• C. $\frac72$
• D. $\frac{37}{12}$

4. A uniform variable on $\{1,\ldots,n\}$ has variance 2. Find $n$.

• A. $4$
• B. $6$
• C. $5$
• D. $25$

5. A uniform variable on $\{1,\ldots,n\}$ has mean 12.5. Find $n$.

• A. $25$
• B. $12$
• C. $13$
• D. $24$