Genuinely discrete discrete probability

Genuinely discrete discrete probability<br /> <br /> What “genuinely discrete” methods can be used with discrete random variables?<br /> <br /> When we first learn probability, we start with discrete random variables – experiments whose outcomes take values are non-negative whole numbers. But we then move on to continuous random variables, where we have richer techniques and results – like moments, scaling, shifting, the law of large numbers, the vital importance of the normal distribution, and the central limit theorem.<br /> <br /> But what if we instead try to stay in those “early days” of learning probability, and stick firmly to the integers, looking for “genuinely discrete” ideas? We might then look at factorial moments, the probability generating function, “thinning”, the vital importance of the Poisson distribution, and the “law of thin numbers”.<br /> <br /> There are plenty of easy-to-state problems regarding “genuinely discrete” discrete probability that have not received the attention they deserve. What is the discrete equivalent of the normal distribution? Which distributions are changed the least by adding independent copies? What symmetries can we observe between high-variance and low-variance distributions? Which discrete random variables are the “most random”?

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly Please state clearly in the Planned Course of Study section that you are applying for is <em><strong>PHD Mathematics (Statistics) FT</strong></em>, in the research information section that the research degree you wish to be considered for is “Genuinely discrete discrete probability” as well as <a href="https://eps.leeds.ac.uk/maths/staff/5707/dr-matthew-aldridge">Dr Matthew Aldridge</a> as your proposed supervisor <em><strong>and in the finance section, please state clearly the funding that you are applying for, if you are self-funding or externally sponsored.</strong></em></p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing" style="text-align:start; margin-bottom:24px">Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents at the point you submit your application:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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<p style="margin-bottom:12px"><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> (open from October 2024 for October 2025 entry) and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a> are available to UK applicants. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> –<a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">The School of Mathematics Scholarships</a> are available to all International applicants.  The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China (open from October 2024 for October 2025 entry). The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><em><strong>Important:</strong></em>  Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are <em><strong>not</strong></em> covered under this studentship.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about applications, contact our admissions team: <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a><br /> For questions about the research project, contact <a href="mailto:m.aldridge@leeds.ac.uk">Dr Matthew Aldridge</a></p>