Among other applications, a gamma distribution answers the question: "If the average time (or other quantity) between events is β, what is the probability that x time will elapse before α events occur?"
The exponential distribution is a special case of the gamma distribution where α = 1. The question is easily rephrased as: "If the average time before an event occurs is β, what is the probability that x time will elapse before the event occurs?"
My textbook defines the chi-squared distribution as a special case of the gamma distribution where α = v/2 and β = 2 where v is a positive integer, but the significance of these numbers is not clear to me. Can the question in the first paragraph be rephrased to fit the chi-squared distribution in the same way I rephrased it to fit the exponential distribution?