Question

please answer all

1. (a) A certain species of bird always lays 3 eggs in the spring, but it is not guaranteed that all of the eggs it lays will hatch. Scientists think that a model for the nunber, X, of eggs that hatch has a probability distribution given by 0 where θ is a parameter to be estimated. i) Given that at least one egg hatches, determine the probability that all three eggs in a nest hatch. 2 marks 3 marks ii) Find the method of moments estimator for the parameter 8 iii) One spring a scientist monitors 20 nests and records how many eggs hatch in each nest. The scientist 's data are listed below in increasing order 000001 1 1 1 22 2 3 333 3333 Use these data to determine the maximum likelihood estimate fr θ. [5 marks! iv) Suppose that the parameter 0 2/5. Deternine the probability that in a random Note: You may assume that the number of eggs hatched in a nest is independent sample of 15 nests, there are at least 5 nests in which no eggs hatch. of the numbers hatched in the other nests. 4 marks) (b) In a separate study, scientists discovered that 70% of a certain species of bird migrate to Northern Africa in winter, and the remaining 30% migrate to Southern Europe. Birds that migrate to Northern Africa have a 25% chance of picking up a certain parasite before returning to Britain, and birds that migrate to Southern Europe have a 15% chance of picking up the parasite before returning to Britain. i) Determine the probability that a bird chosen at random from this species has 3 marks picked up the parasite while migrating over the winter. ii) Given that a bird is carrying the parasite, determine the probability that the bird 3 marks) migrated to Northern Africa over the winter Total 20 marks)

Answer 1

that-hatch 2 χ> a. 2 Scan with

식욕 ty).一ㄧ影3t-서' M-t Lo 201 So it. QC -t 2e 1-20 Scanned Ro

P加 0 0 Scanned wih amscarthe

Date no? hahh 3338 0 16 42 70'i o south 0 22 2 canne