Mean and variance of a CRV Quiz

1. $f(x)=\frac{x}{2}$ for $0\le x\le2$. Find $E(X)$.

• A. $1$
• B. $\frac43$
• C. $\frac23$
• D. $2$

2. $E(X)=3$ and $E(X^2)=11$. Find $\text{Var}(X)$.

• A. $8$
• B. $2$
• C. $5$
• D. $-2$

3. $\text{Var}(X)=5$. Find $\text{Var}(3X-7)$.

• A. $8$
• B. $15$
• C. $38$
• D. $45$

4. $E(X)=10$. Find $E(5-2X)$.

• A. $-15$
• B. $25$
• C. $-20$
• D. $15$

5. $f(x)=\frac{3x^2}{8}$ for $0\le x\le2$. Find $E(X^{-1})$.

• A. $\frac34$
• B. $\frac38$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$