The continuous uniform distribution Quiz

1. $X\sim U[0,10]$. Find $P(X>7.5)$.

• A. $0.75$
• B. $0.7$
• C. $0.25$
• D. $0.1$

2. $X\sim U[4,10]$. Find $\text{Var}(X)$.

• A. $3$
• B. $36$
• C. $6$
• D. $12$

3. $X\sim U[1,5]$. What is $F(x)$ for $1\le x\le5$?

• A. $\frac x5$
• B. $\frac x4$
• C. $\frac{x-1}{5}$
• D. $\frac{x-1}{4}$

4. $X\sim U[0,6]$. Find $P(1<X<4)$.

• A. $\frac13$
• B. $\frac12$
• C. $\frac23$
• D. $\frac16$

5. $X\sim U[a,b]$ has $E(X)=10$ and $\text{Var}(X)=3$. Find $a$ and $b$.

• A. $a=8$, $b=12$
• B. $a=5$, $b=15$
• C. $a=7$, $b=13$
• D. $a=4$, $b=16$