4.14 Discrete and continuous random variables Quiz

1. $\mathrm{Var}(X) = 4$. Find $\mathrm{Var}(3X - 2)$.

• A. 10
• B. 12
• C. 34
• D. 36

2. $f(x) = kx$ for $0 \le x \le 2$ and 0 otherwise is a pdf. Find $k$.

• A. $\frac{1}{2}$
• B. $2$
• C. $\frac{1}{4}$
• D. $1$

3. $X$ has pdf $f(x) = 3x^2$ for $0 \le x \le 1$. Find $E(X)$.

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $1$
• D. $\frac{3}{5}$

4. A discrete random variable has $E(X) = 2$ and $E(X^2) = 5$. Find $\mathrm{Var}(X)$.

• A. 3
• B. 9
• C. 1
• D. 4

5. $X$ has pdf $f(x) = 2x$ for $0 \le x \le 1$. Find the median, to 3 significant figures.

• A. 0.500
• B. 0.667
• C. 0.250
• D. 0.707