Probability density functions Quiz

1. A continuous random variable has pdf $f(x)=\frac{1}{4}$ for $0\le x\le4$. Find $P(1<X<3)$.

• A. $\frac12$
• B. $\frac14$
• C. $\frac34$
• D. $\frac18$

2. The pdf of $X$ is $f(x)=kx$ for $0\le x\le2$. Find $k$.

• A. $\frac14$
• B. $2$
• C. $\frac12$
• D. $1$

3. Which statement about a continuous random variable $X$ is true?

• A. $P(X=3)=f(3)$
• B. $P(X<3)<P(X\le3)$
• C. $f(x)$ can never exceed 1
• D. $P(X=3)=0$

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

• A. $1$
• B. $2$
• C. $\sqrt2$
• D. $\frac{\sqrt2}{2}$

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

• A. $\frac18$
• B. $\frac78$
• C. $\frac38$
• D. $\frac58$