EXAMPLE 5.7a The lifetime of a battery is exponentially distributed with rate . If a stereo cassette

EXAMPLE 5.7a The lifetime of a battery is exponentially distributed with rate λ. If a stereo cassette requires one battery to operate, then the total playing time one can obtain from a total of n batteries is a gamma random variable with parameters (n, λ). ■

Figure 5.11 presents a graph of the gamma (α, 1) density for a variety of values of α. It should be noted that as α becomes large, the density starts to resemble the normal density.

This is theoretically explained by the central limit theorem, which will be presented in the next chapter.