Mean, variance, mode, median and quartiles Quiz

1. $f(x)=2x$ for $0\le x\le1$. Find $E(X)$.

• A. $\frac23$
• B. $\frac12$
• C. $1$
• D. $\frac34$

2. $E(X)=3$ and $E(X^2)=10$. Find $\text{Var}(X)$.

• A. $10$
• B. $7$
• C. $1$
• D. $3$

3. $F(x)=\frac{x^2}{9}$ for $0\le x\le3$. Find the median.

• A. $1.5$
• B. $2$
• C. $2.25$
• D. $2.12$

4. $f(x)=\frac34x(2-x)$ for $0\le x\le2$. Find the mode.

• A. $\frac12$
• B. $1$
• C. $\frac34$
• D. $2$

5. $F(x)=\frac{x^2}{16}$ for $0\le x\le4$. Find the lower quartile.

• A. $1$
• B. $3$
• C. $2$
• D. $2\sqrt2$