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The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
The earliest known mention of the gambler's ruin problem is a letter from Blaise Pascal to Pierre Fermat in 1656 (two years after the more famous correspondence on the problem of points). [2] Pascal's version was summarized in a 1656 letter from Pierre de Carcavi to Huygens:
In the letters, Pascal's tone combines the fervor of a convert with the wit and polish of a man of the world. Their style meant that, quite apart from their religious influence, the Provincial Letters were popular as a literary work. Adding to that popularity was Pascal's use of humor, mockery, and satire in his arguments.
The following is the 1961–62 network television schedule for the three major English language commercial broadcast networks in the United States. The schedule covers primetime hours from September 1961 through April 1962. The schedule is followed by a list per network of returning series, new series, and series cancelled after the 1960–61 ...
Pascal's triangle, rows 0 through 7. The hockey stick identity confirms, for example: for n =6, r =2: 1+3+6+10+15=35. In combinatorics , the hockey-stick identity , [ 1 ] Christmas stocking identity , [ 2 ] boomerang identity , Fermat's identity or Chu's Theorem , [ 3 ] states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then
The following is the 1969–70 network television schedule for the three major English language commercial broadcast networks in the United States. The schedule covers primetime hours from September 1969 through August 1970. The schedule is followed by a list per network of returning series, new series, and series cancelled after the 1968–69 ...
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The following is the 1966–67 network television schedule for the three major English language commercial broadcast networks in the United States. The schedule covers primetime hours from September 1966 through August 1967. The schedule is followed by a list per network of returning series, new series, and series cancelled after the 1965–66 ...