The continuous uniform distribution Quiz

1. $X\sim U[4,10]$. What is $\mathrm{E}(X)$?

• A. $3$
• B. $6$
• C. $7$
• D. $14$

2. $X\sim U[0,12]$. What is $\mathrm{Var}(X)$?

• A. $12$
• B. $1$
• C. $6$
• D. $144$

3. $X\sim U[1,5]$. What is $\mathrm{P}(X<2.5)$?

• A. $0.5$
• B. $0.3$
• C. $0.25$
• D. $0.375$

4. For $X\sim U[a,b]$ and $a\le x\le b$, the cumulative distribution function is

• A. $\frac{1}{b-a}$
• B. $\frac{x-a}{b-a}$
• C. $\frac{x}{b}$
• D. $\frac{b-x}{b-a}$

5. $X\sim U[a,b]$ has mean $10$ and $b-a=6$. Find $a$.

• A. $7$
• B. $16$
• C. $13$
• D. $4$