The length of time a particular smartphone's battery lasts...

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.
a. What is the standard deviation?
b. What is the parameter $m$ ?

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Key Concepts

Exponential Distribution

The exponential distribution is a continuous probability model commonly used to represent the time between events in a Poisson process. It has the special property that the probability of an event occurring in the next period is independent of how much time has already elapsed, which is known as the memoryless property.

Standard Deviation in Exponential Distribution

For an exponential distribution, the standard deviation is equal to its mean. This results from its mathematical properties, meaning that if the average (mean) time between events is known, the spread or variability of the distribution, measured by the standard deviation, is the same numerical value.

Parameterization of the Exponential Distribution

The exponential distribution can be parameterized either with a rate parameter (?) or a scale parameter (m). The rate parameter is defined as the reciprocal of the mean, ? = 1/m, while the scale parameter m directly represents the mean of the distribution. Understanding this relationship is essential for correctly interpreting the distribution's probability density function.

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