Your goal in this assignment is to estimate the age of the universe based on an estimate of the Hubble constant n and to quantify the quality of the estimate. The age of the universe can be expressed in years as 9=c n s/year) Assumptions 1 f(h;a,3)= ha-le- 3aT(a) h>0 Note that this exam works with the gamma density as parameterized in the textbook - that is. with shape parameter a and scale parameter . Assume further that the common mean is in fact the Hubble constant; denote this by n = E[H,] Problems 1. The following parts guide you through finding the distribution of 6. (a) Show that c-1H has a gamma (na, ne) distribution. Write its density. (b) Show that 6 = cH-1 has an inverse gamma distribution with density (cn)na -na-le-s For short, U ~ IG (na, cn). (Hint: for x > 0, the function is monotone decreasing.)