BASIC PROPERTIES OF THE EXPONENTIAL DISTRIBUTION

The following interactive animation illustrates the basic properties of the exponential distribution.

An exponential distribution is displayed.

Recall that it is entirely defined by the value of the unique positive parameter λ. The value of Lambda is displayed to the right of the frame.

Mean

The mean of the distribution is µ = 1/λ.

The value of the mean is indicated by the vertical green line. To change this value (and that of Lambda as well), slide the upper end of this line with your mouse. Note that the product of Lambda and the Mean is always 1.

Standard deviation

The variance of the distribution is σ² = 1/λ².

The standard deviation is therefore σ = 1/λ.

Two short and thick blue vertical ticks are positionned on either side of the mean. Their (common) distance to the mean is σ.

Observe that the left standard deviation tick is always positioned at "0" whatever the value of λ. This is of course because the mean and the standard deviations are equal.

Mode

The largest density is obtained for x = 0 (intercept of the curve). It is equal to λ, and is displayed.