Rectangular distribution Quiz

1. $X$ is rectangular on $[0,12]$. Find $\mathrm{P}(X>9)$.

• A. $\frac34$
• B. $\frac13$
• C. $\frac14$
• D. $\frac{1}{12}$

2. $X$ is rectangular on $[1,7]$. Find $\mathrm{E}(X)$.

• A. $4$
• B. $3$
• C. $6$
• D. $\frac14$

3. $X$ is rectangular on $[0,6]$. Find $\mathrm{Var}(X)$.

• A. $\frac12$
• B. $\frac32$
• C. $9$
• D. $3$

4. Which statement describes a condition for a rectangular model?

• A. Values cluster at the centre of the interval
• B. The mean equals the variance
• C. Equal-width intervals within $[a,b]$ have equal probability
• D. The probability falls as $x$ increases

5. A rectangular distribution has mean $10$ and variance $12$. Find $a$ and $b$.

• A. $a=7,\ b=13$
• B. $a=4,\ b=16$
• C. $a=8,\ b=12$
• D. $a=2,\ b=18$