mathematics

Patrick Billingsley

Patrick Billingsley 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 Patrick Billingsley rather than just read about it. In short: Patrick Paul Billingsley (May 3, 1925 – April 22, 2011) was an American mathematician noted for his books in advanced probability theory and statistics. Academic career Billingsley was born and raised in Sioux Falls, South Dakota, and graduated from the United States Naval Academy in 1946.

Key takeaways

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

Reference excerpt

Patrick Paul Billingsley (May 3, 1925 – April 22, 2011) was an American mathematician noted for his books in advanced probability theory and statistics.

Academic career Billingsley was born and raised in Sioux Falls, South Dakota, and graduated from the United States Naval Academy in 1946. After earning a Ph.D. in mathematics at Princeton University in 1955, he was attached to the NSA until his discharge from the Navy in 1957. In 1958 he became a professor of mathematics and statistics at the University of Chicago, where he served as chair of the Department of Statistics from 1980 to 1983, and retired in 1994. In 1964–65 he was a Fulbright Fellow and visiting professor at the University of Copenhagen. In 1971–72 he was a Guggenheim Fellow and visiting professor at the University of Cambridge (Peterhouse). From 1976 to 1979 he edited the Annals of Probability. In 1983 he was president of the Institute of Mathematical Statistics. He was given the Lester R. Ford Award for his article "Prime Numbers and Brownian Motion." He was elected a Fellow of the American Academy of Arts and Sciences in 1986. In Young Men and Fire, fellow University of Chicago professor Norman Maclean wrote about Billingsley that "he is a distinguished statistician and one of the best amateur actors I have ever seen".

Books Statistical Inference for Markov Processes (1961) Ergodic Theory and Information (1965) Convergence of Probability Measures (1st Edition 1968, 2nd Edition 1999) The Elements of Statistical Inference (with David L. Huntsberger, 1986) Probability and Measure (1st Edition 1976, 2nd Edition 1986, 3rd Edition, 1995, Anniversary Edition 2012 )

Stage plays Three Magic Keys, Taliesin (1964) The Pirates of Penzance, Pirate (1966) Read Me a Story (1966) Clue of the Circus Clowns, Circus Master (1968) Finian's Rainbow, Buzz Collins (1968) Beadle-Levi Show (parody of The Homecoming) (1968) Guys and Dolls, Arvide Abernathy (1969) We Bombed in New Haven (Court Theatre, 1970) Victorian Children (1970) Vaudeville Show, singer (1970) The Threepenny Opera, street singer (1970) Four Plays of Fantasy and the Unusual (1970) Moulin Rouge (1971) Oh, What a Lovely War! (1973) Midsummer Night's Dream, Theseus (Court Theatre, 1973) The Caretaker, Aston (Court Theatre, 1973) The Father, The Captain (1974) Murder in the Cathedral, First Knight (1974) Twelfth Night, Feste (Court Theatre, 1974) The Same Room, Tom Ferris (1975) Dracula, Dr. Seward (1975) Much Ado about Nothing, Balthazar and Friar Frances (Court Theatre, 1975) Exits and Entrances (1976) Trifles, Sheriff Peters (1976) The Lover, Richard-Max (Court Theatre, 1977) The Tempest, Alonzo (Court Theatre, 1977) She Stoops to Conquer, Mr. Hardcastle (Court Theatre, 1978) Measure for Measure, The Duke (Court Theatre, 1979) Mrs. Warren's Profession, Rev. Samuel Gardiner (Court Theatre, 1980) Equus, Dr. Dysart (Court Theatre, 1980) The Seagull, Sorin (Court Theatre, 1981) Twelfth Night, Antonio (Body Politic Theatre, 1981) Under Milk Wood, Rev. Eli Jenkins et al. (Court Theatre, 1982) The First Night of Pygmalion, Beerbohm-Tree et al. (Court Theatre, 1982) Midsummer Night's Dream, Peter Quince (Court Theatre, 1983) Much Ado about Nothing, Leonato (Court Theatre, 1984) Heartbreak House, Mazzini Dunn (Court Theatre, 1985) Every Good Boy Deserves Favor, KGB colonel (Court Theatre, 1985) The Birthday Party, Petey (1978 and 1985) Arms and the Man, Major Petkoff (Court Theatre, 1985) Moonlight Daring Us to Go Insane, J. Earl Sheets (Body Politic Theatre, 1987) Coastal Disturbances, R. Hamilton Adams (Body Politic Theatre, 1987)

Films The Fury (1978) - CIA agent Lander My Bodyguard (1980) - Biology Teacher Somewhere in Time (1980) - Professor One More Saturday Night (1985) - Mr. McGrath The Untouchables (1987) - Bailiff #2

Television Dummy (1978, TV Movie) - Dr. Morris Flesh and Blood (1978) - Boxing official The Children Nobody Wanted (1981) - Preacher The Dollmaker (1983) - Cooper The Last Leaf – A Parable of Easter (1983, Short) - Dr. Winchester The Private Eye (1983) - Guard Murder Ordained (1986) - Ray Call Jack and Mike (episode) (1986) - Judge Sable (1987) - Sullivan The Father Clements Story (1987, TV Movie) - Father Donovan (final film role)

Death He died in 2011, aged 85, in his Hyde Park, Chicago home. He was survived by his children, Franny, Patty, Julie, Marty and Paul, and his companion, Florence Weisblatt. His wife of nearly 50 years, social activist Ruth Billingsley, died in 2000.

References

External links

Patrick Billingsley at IMDb Obituary in the Chicago Tribune Patrick Billingsley, probability theorist and actor, 1925–2011

Illustrations

Worked examples

Example 1 — a first encounter with Patrick Billingsley

Start with the simplest possible case. Write down what Patrick Billingsley 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 Patrick Billingsley 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 Patrick Billingsley 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 Patrick Billingsley

In research: Patrick Billingsley 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 Patrick Billingsley 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: Patrick Billingsley is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2011 deaths, 20th-century American male actors, so understanding it makes those chapters shorter.
In everyday life: Look for Patrick Billingsley 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 Patrick Billingsley in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Patrick Billingsley 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 Patrick Billingsley out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Patrick Billingsley in simple terms?

Patrick Paul Billingsley (May 3, 1925 – April 22, 2011) was an American mathematician noted for his books in advanced probability theory and statistics. Academic career Billingsley was born and raised in Sioux Falls, South Dakota, and graduated from the United States Naval Academy in 1946.

Why does Patrick Billingsley 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 Patrick Billingsley?

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 Patrick Billingsley.