Quasars Light from quasars can reach Earth from the edge of the visible universe. Viewed from Earth, the sky can be divided into "square degrees". Assume quasars occur in a small patch of sky according to a Poisson process. ("Occurs" means "when the quasar first can be observed by astronomers".) On average, there are 2 quasars per year per thousand square degrees of sky. The numbers of quasars in non-overlapping patches of sky in a year are independent and the numbers of quasars in a patch of sky in non-overlapping periods of time are independent. The probability of simultaneous quasars is zero. NOTES: The square degree is a measure of solid angle. There are 41,253 square degrees in a sphere. Your professor has no idea whether the assumption of a Poisson process for quasar occurrence is realistic but the assumption seems reasonable because a quasar occurs at the center of a galaxy; the number of galaxies is very large (estimated to be one or two trillion); and the universe is essentially "flat", implying that at large scales, it looks the same in all directions. The value of the Poisson parameter was assumed for convenience in the question. We'd need an astronomer to give us a realistic estimate

What is the expected number of quasars in a given one thousand square degree patch of sky in a year? One decimal What is the expected number of quasars in a year? There are 41,253 square degrees in a sphere (from Earth, quasars occur on a sphere). Three decimals What is the probability of one guasar occurring in a one thousand square degree patch of sky, during a year? Four decimals What is the probability of at least one quasar occurring in a one thousand square degree patch of sky, during a year? Four decimals What is the expected number of quasars in a given one thousand square degree patch of sky, in a three-year period? One decimal What is the probability of 3 guasa rs occurring in a one thousand square degree patch of sky, during a three-year period? Four decimals What is the probability of one quasar occurring in a one thousand square degree patch of sky, each year, for three consecutive years? Four decimals COMMENT: Think about why the answers to this question and the previous one are different! Consider the patch of sky corresponding to the constellation Hydra, which covers approximately 1.3 thousand square degrees. What is the probability that there will be m guasar in that patch of sky in the next year? Four decimals