mathematics

Stephen Mitchell Samuels

Stephen Mitchell Samuels is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Stephen Mitchell Samuels rather than just read about it. In short: Stephen Mitchell Samuels (1938, Brooklyn – July 26, 2012, Indiana) was a statistician and mathematician, known for his work on the secretary problem and for the Samuels Conjecture involving a Chebyshev-type inequality for sums of independent, non-negative random variables. After completing his undergraduate degree at Massachusetts Institute of Technology, he became a graduate student at Stanford University.

Key takeaways

Stephen Mitchell Samuels belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Stephen Mitchell Samuels to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Stephen Mitchell Samuels from memory before moving on to harder problems.

Reference excerpt

Stephen Mitchell Samuels (1938, Brooklyn – July 26, 2012, Indiana) was a statistician and mathematician, known for his work on the secretary problem and for the Samuels Conjecture involving a Chebyshev-type inequality for sums of independent, non-negative random variables. After completing his undergraduate degree at Massachusetts Institute of Technology, he became a graduate student at Stanford University. There he received his Ph.D. in 1964 with a thesis supervised by Samuel Karlin. Samuels joined in 1964 the faculty of Purdue University and retired there in 2003 as professor emeritus of statistics and mathematics. He did research on various topics in probability theory and its applications, dynamic optimization, and disclosure risk assessment for statistical microdata.

Selected publications Samuels, S. M. (1965). "On the Number of Successes in Independent Trials". The Annals of Mathematical Statistics. 36 (4): 1272–1278. doi:10.1214/aoms/1177699998. 1965 Jogdeo, Kumar; Samuels, S. M. (1968). "Monotone Convergence of Binomial Probabilities and a Generalization of Ramanujan's Equation". The Annals of Mathematical Statistics. 39 (4): 1191–1195. doi:10.1214/aoms/1177698243. 1966 Samuels, S. M. (1968). "Randomized Rules for the Two-Armed-Bandit with Finite Memory". The Annals of Mathematical Statistics. 39 (6): 2103–2107. doi:10.1214/aoms/1177698038. JSTOR 2239307. 1968 Samuels, S. M. (1974). "A Characterization of the Poisson Process". Journal of Applied Probability. 11 (1): 72–85. doi:10.2307/3212584. JSTOR 3212584. 1974 Gianini, Jacqueline; Samuels, Stephen M. (1976). "The Infinite Secretary Problem". The Annals of Probability. 4 (3): 418–432. doi:10.1214/aop/1176996090. JSTOR 2959244. 1976 Rubin, H.; Samuels, S. M. (1977). "The Finite-Memory Secretary Problem". The Annals of Probability. 5 (4): 627–635. doi:10.1214/aop/1176995774. JSTOR 2243090. 1977 Frank, Arthur Q.; Samuels, Stephen M. (1980). "On an optimal stopping problem of Gusein-Zade". Stochastic Processes and Their Applications. 10 (3): 299–311. doi:10.1016/0304-4149(80)90013-7. 1980 Samuels, Stephen M.; Steele, J. Michael (1981). "Optimal Sequential Selection of a Monotone Sequence from a Random Sample". The Annals of Probability. 9 (6): 937–947. doi:10.1214/aop/1176994265. JSTOR 2243756. 1981 Samuels, Stephen M.; Chotlos, Bay (1986). "A Multiple Criteria Optimal Selection Problem". Lecture Notes-Monograph Series. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Vol. 8. pp. 62–78. doi:10.1214/lnms/1215540289. ISBN 0-940600-09-9. JSTOR 4355521. 1986 Bruss, F. Thomas; Samuels, Stephen M. (1987). "A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options". The Annals of Probability. 15 (2): 824–830. doi:10.1214/aop/1176992175. JSTOR 2244078. 1987 Samuels, Stephen M.; Studden, William J. (1989). "Bonferroni-Type Probability Bounds as an Application of the Theory of Tchebycheff Systems". Probability, Statistics, and Mathematics. pp. 271–289. doi:10.1016/B978-0-12-058470-3.50026-4. ISBN 9780120584703. 1989 Bruss, F. Thomas; Samuels, Stephen M. (1990). "Conditions for Quasi-Stationarity of the Bayes Rule in Selection Problems with an Unknown Number of Rankable Options". The Annals of Probability. 18 (2): 877–886. doi:10.1214/aop/1176990864. hdl:2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/199662. JSTOR 2244322. 1990 Samuels, Stephen M. (1990). "Applications of statistics to Antarctic, non-Antarctic differences". Differences Between Antarctic and Non-Antarctic Meteorites. pp. 74–80. Bibcode:1989LPICo.712..216S. Samuels, Stephen M. (1992). "Secretary Problems as a Source of Benchmark Bounds". Lecture Notes-Monograph Series. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Vol. 22. Institute of Mathematical Statistics. pp. 371–387. doi:10.1214/lnms/1215461963. ISBN 0-940600-29-3. JSTOR 4355753. 1992

References

Worked examples

Example 1 — a first encounter with Stephen Mitchell Samuels

Start with the simplest possible case. Write down what Stephen Mitchell Samuels claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Stephen Mitchell Samuels before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Stephen Mitchell Samuels ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Stephen Mitchell Samuels

In research: Stephen Mitchell Samuels appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Stephen Mitchell Samuels in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Stephen Mitchell Samuels is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 2012 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Stephen Mitchell Samuels outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Stephen Mitchell Samuels in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Stephen Mitchell Samuels means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Stephen Mitchell Samuels out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stephen Mitchell Samuels in simple terms?

Why does Stephen Mitchell Samuels matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Stephen Mitchell Samuels?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Stephen Mitchell Samuels.