We can calculate the probabilities using formulas or Excel. The formulas are:

• $P(\text{at most or less than}) = P(X \le x) = 1 - e^{-\lambda x}$
• $P(\text{at least or more than}) = P(X \ge x) = e^{-\lambda x}$

The Excel calculations are:

• $P(\text{at most or less than}) =\text{EXPON.DIST}(x, \lambda, \text{TRUE})$
• $P(\text{at least or more than}) =1-\text{EXPON.DIST}(x, \lambda, \text{TRUE})$

• Memoryless means that it does not matter how much time has elapsed previously.
• When calculating the odds of a certain amount of time elapsing going forward,
• It’s although the clock resets to zero.
• See Wikipedia‘s explanation of memoryless:
  

  It describes situations where the time you’ve already waited for an event doesn’t affect how much longer you’ll have to wait

The following metrics apply to exponential distributions:

• $x = \text{time between events}$
• $\lambda = \text{lambda}=\text{number of events per time unit}$
• The mean is: $\mu = \frac{1}{\lambda}$
• The standard deviation is also: $\frac{1}{\lambda}$
• The variance is: $\sigma^2 = \frac{1}{\lambda ^2}$
• The distribution is right skewed and the skewness = 2.

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