Statistics (Poisson Distribution, Exponential Distribution)

Question

Is lambda (λ) parameter used in Poisson Distribution, Exponential Distribution the same.
If say λ = 4 customers per hour,
then Expected value, E(possion X) = rate = λ = 4,

and E(exponential x) = Average waiting time = 1/λ = 1/4.

Is this correct?

Answer 1

Correct. 

E[ Exponential ]=1/E[ Poisson per unit time ]

If $,\; \lambda =4$ patients per hour:

• Poisson mean = 4 patients (per hour)

• Exponential mean = $1/4$ hour (time between patients)

 

Remember : 

whenever you identify the event rate $\lambda$, you can switch between “how many” (multiply by time) and  “how long” (taking reciprocal).

 

I hope this Concept is Clear.