Exponential distribution model, pdf and CDF Quiz

1. $X$ has an exponential distribution with $\lambda=2$. Find $\mathrm{P}(X>1)$.

• A. $1-e^{-2}$
• B. $2e^{-2}$
• C. $e^{-2}$
• D. $e^{-1}$

2. Which expression is the cdf of an exponential distribution?

• A. $e^{-\lambda x}$
• B. $1-e^{-\lambda x}$
• C. $\lambda e^{-\lambda x}$
• D. $1-\lambda e^{-\lambda x}$

3. Which situation is suitable for an exponential model?

• A. The time between random independent events at a constant rate
• B. The number of events in a fixed time
• C. The height of adults
• D. The time until a component wears out with age

4. $X$ is exponential with $\lambda=0.5$. Find $\mathrm{P}(X<2)$.

• A. $0.368$
• B. $0.865$
• C. $0.135$
• D. $0.632$

5. $f(x)=ke^{-4x}$ for $x\ge0$ is a pdf. Find $k$.

• A. $4$
• B. $\frac14$
• C. $e^4$
• D. $2$