Let H denote the true Hubble constant. The age of the universe can be expressed in years as ? = c/H where c is the conversion factor (Mpc/km) (s/year) = 978, 440, 076, 094.

Q. Determine a way to estimate the bias of ^? under the gamma model. Does it seem large in context?

The Hubble constant is a fundamental cosmological parameter used to describe the size and age of the universe. It relates the distance and velocity of objects relative to earth via the relationship: s=Hd Astrophysicists estimate the Hubble constant from observed ratios 3 for a sample of galaxies. Though seemingly simple, the measurements of these two quantities velocity and distance are challenging to obtain with accuracy, and continue to be rened (see a recent article}. The primary objective of the Hubble Space Telescope (HST), launched in 1990, is to collect data that will lead to more precise estimates of the Hubble constant. Velocity is calculated from spectroscopic measurements, which are less complicated to obtain compared with distance measurements. For the latter, \"[r]eliable 'distance indicators", such as variable stars and supernovae, must be found in a sample of galaxies that are far enough away that motions due to local gravitational inuences are negligibly small\" (quote from Space Science Short}. In 2001, Freedman e1! oi. published a set of measurements based on novel distance indicators and HST data; distancevelocity ratios from measurements for 36 type la supernovae using their method of calculation are shown in Figure l. 035 U06 density E 0.02 000 65 ?0 ?5 BO 35 velocityldistanoa Figure l: Histogarn of H values from 36 type 1a supernovae, with a smooth overlay to aid in visualizing the shape of the distribution. The sample mean and variance are H = 72.1861 and 3%, = 233353