How are Exponential and Gamma distribution related?

Question

Suppose the survival time X in weeks of a randomly selected male mouse exposed to 240 rads of gamma radiation has a gamma distribution with 𝛼 = 8 and 𝛽 = 15. What is the probability that a mouse survives (a) between 60 and 120 weeks (b) at least 30 weeks (c) more than 50 weeks

Answer 1

As 8*15 = 120, my assumption is that B is a scale parameter rather than a rate parameter. Otherwise, these values become very small. In Wikipedia, for example, when B is used rather than k, it is assumed to be a rate parameter.

Then, packages will provide these probabilities, with the same type of parameter setup as with other distributions.

For example, in Excel, our answers are

=GAMMA.DIST(120,8,15,1)-GAMMA.DIST(60,8,15,1) = .4959

= 1 - GAMMA.DIST(30,8,15,1) = .9989

= 1 - GAMMA.DIST(50,8,15,1) = .9792

This assumes that we aren't trying to make some kind of continuity correction.

With a continuity correction, one would get

=GAMMA.DIST(120.5,8,15,1)-GAMMA.DIST(59.5,8,15,1) = .5025

= 1 - GAMMA.DIST(29.5,8,15,1) = .9990

= 1 - GAMMA.DIST(50.5,8,15,1) = .9781

I only thought of making continuity corrections because of the use of at least and more than.