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Assignment 2 (M365)
Problem 3. Let N be the collection of all null sets in R and let L be the collection of all full sets, i.e. those sets A for which Ac ∈ N . Consider their union F = N ∪ L. Is F a σ-field? Justify your answer.
(i) One day, you telephone the father and ask: “Is there at least one boy among your children?” He answers: “Yes”. Describe the probability space and calculate the probability that the both children are boys.
Remark: you can accept that any one new born child is a boy or a girl equiprobably and independently of anything else; similarly, the father has equal chances (independent of anything else) to take any one (and only one) of his children for a walk.
You also affirm that
- the work you are submitting is your own and you have not commissioned production of the work from a third party or used artificial intelligence software in an unacceptable manner to generate the work*,
- you have not copied material from another person or source, nor committed plagiarism, nor fabricated, falsified or embellished data when com pleting the attached piece of work.
- you have not colluded with any other student in the preparation and/ or production of this work.
Marks achieved on this assessment remain provisional until they are ratified by the Board of Examiners in June 2024. Please note that your submission will be analysed by Turnitin for plagiarism and an Artificial Intelligence detection tool.