Cumulative distribution functions Quiz

1. $F(x)=\frac{x^2}{4}$ for $0\le x\le2$. Find $P(X>1)$.

• A. $\frac14$
• B. $\frac12$
• C. $\frac34$
• D. $1$

2. $F(x)=\frac{x^3}{8}$ for $0\le x\le2$. Find $f(x)$.

• A. $\frac{3x^2}{8}$
• B. $\frac{x^4}{32}$
• C. $\frac{x^3}{8}$
• D. $\frac{3x^2}{4}$

3. Which of these could NOT be a cdf?

• A. A function that rises from 0 to 1
• B. A function with $F(x)=1$ for large $x$
• C. A function with $F(x)=0$ for small $x$
• D. A function that decreases somewhere

4. $F(x)=\frac{x^2}{4}$ for $0\le x\le2$. Find the median.

• A. $1$
• B. $\sqrt2$
• C. $2$
• D. $\frac12$

5. $f(x)=\frac14$ for $0\le x\le4$. Find $F(x)$ for $0\le x\le4$.

• A. $\frac14$
• B. $\frac{x^2}{8}$
• C. $\frac x4$
• D. $4x$