Question

If the number of telephone calls coming into a telephone exchange between 10 AM and 11 AM follows Poisson distribution with parameter 2 then the probability of obtaining at least one call in that time interval is

• A. $e^{-2}$
• B. $(1-e^{-2})$
• C. $2e^{-2}$
• D. $3e^{-2}$

Answer 1

Answer: (B)

$(1-e^{-2})$

By using Poisson distribution,
$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$
$\mu$: The mean number of successes that occur in a specified region(Parameter)
x: The actual number of successes that occur in a specified region.
P(x;$\mu$ ): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is $\mu$
$P(x\ge 1;\mu )=1-P(x=0;\mu )$
$\mu =2$
$x=0$ (No call comes)
$P(x\ge 1;2)=1-P(x=0;2)=1-\frac{e^{-2}{2}^0}{0!}=1-e^{-2}$