Mean and variance, and link to Poisson processes Quiz

1. $X$ is exponential with $\lambda=0.25$. Find $\mathrm{E}(X)$.

• A. $0.25$
• B. $16$
• C. $4$
• D. $0.0625$

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

• A. $4$
• B. $2$
• C. $0.25$
• D. $0.5$

3. Calls arrive as a Poisson process at 6 per hour. What is the mean time between calls?

• A. 6 minutes
• B. $\frac16$ minute
• C. 60 minutes
• D. 10 minutes

4. Which statement about an exponential distribution is correct?

• A. The standard deviation is twice the mean
• B. The standard deviation equals the mean
• C. The standard deviation is the mean squared
• D. The standard deviation is the variance squared

5. $X$ is exponential with $\lambda=2$. Find $\mathrm{E}(X^2)$.

• A. $0.25$
• B. $1$
• C. $0.5$
• D. $2$