rolling roll call of the states

Examples of rolling roll call of the states in the following topics:

• Selecting Candidates

  • The presidential candidates of the two major political parties in the United States are formally confirmed during the Democratic National Convention and Republican National Convention.
  • Such formulas usually consider the population of a given state, the state's previous presidential voting patterns, and the number of Congressional representatives or government officials in a state who are members of the party.
  • The voting method used during a convention is known as a rolling roll call of the states.
  • The spokespersons of the states are called upon in alphabetical order by state name to announce their delegation count or to pass.
  • The decision to pass is usually made beforehand to give either the delegation of the presidential or vice presidential candidates' home state the honor of casting the majority-making vote.

• Rolling Without Slipping

  • The motion of rolling without slipping can be broken down into rotational and translational motion.
  • To relate this to a real world phenomenon, we can consider the example of a wheel rolling on a flat, horizontal surface.
  • When an object is rolling on a plane without slipping, the point of contact of the object with the plane does not move.
  • In mathematical terms, the length of the arc is equal to the angle of the segment multiplied by the object's radius, R.
  • A body rolling a distance of x on a plane without slipping.

• The Paradox of the Chevalier De Méré

  • One of the problems he was interested in was called the problem of points.
  • Getting a pair of sixes on a single roll of two dice is the same probability of rolling two sixes on two rolls of one die.
  • The probability of rolling two sixes on two rolls is $\frac{1}{6}$ as likely as one six in one roll.
  • To make up for this, a pair of dice should be rolled six times for every one roll of a single die in order to get the same chance of a pair of sixes.
  • Therefore, rolling a pair of dice six times as often as rolling one die should equal the probabilities.

• Rock and Roll

  • The rock music of the 1960s had its roots in rock and roll, but also drew strongly on genres such as blues, folk, jazz, and classical.
  • Rock music is a genre of popular music that developed during the 1960s, particularly in the United Kingdom and the United States.
  • In 1964, the Beatles achieved a breakthrough to mainstream popularity in the United States .
  • The "Beat Generation" had a pervasive influence on the development of psychedelic rock and roll and pop music; these included the Beatles, Bob Dylan and Jim Morrison.
  • Several rock historians have claimed that rock and roll was one of the first music genres to define an age group, giving teenagers a sense of belonging.

• Introduction to defining probability (special topic)

  • What is the chance of getting 1 when rolling a die?
  • What is the chance of getting a 1 or 2 in the next roll?
  • What is the chance of getting either 1, 2, 3, 4, 5, or 6 on the next roll?
  • Since the chance of rolling a 2 is 1/6 or 16.6%, the chance of not rolling a 2 must be 100% - 16.6% = 83.3% or 5/6.
  • The fraction of die rolls that are 1 at each stage in a simulation.The proportion tends to get closer to the probability 1=6 0:167 as the number of rolls increases.

• Probability

  • The probability of an outcome is the proportion of times the outcome would occur if we observed the random process an in finite number of times.
  • Let $\bar{\rho}_n$ be the proportion of outcomes that are 1 after the first $n$ rolls.
  • As the number of rolls increases, $\bar{\rho}_n$ will converge to the probability of rolling a 1, p = $\frac{1}{6}$ .
  • However, these deviations become smaller as the number of rolls increases.
  • Above we write p as the probability of rolling a 1.

• What Does the Law of Averages Say?

  • The expected value of a roll is 3.5, which comes from the following equation:
  • According to the law of large numbers, if a large number of six-sided dice are rolled, the average of their values (sometimes called the sample mean) is likely to be close to 3.5, with the accuracy increasing as more dice are rolled .
  • However, in a small number of rolls, just because ten 6's are rolled in a row, it doesn't mean a 1 is more likely the next roll.
  • This shows a graph illustrating the law of large numbers using a particular run of rolls of a single die.
  • As the number of rolls in this run increases, the average of the values of all the results approaches 3.5.

• Disjoint or mutually exclusive outcomes

  • On the other hand, the outcomes 1 and "rolling an odd number" are not disjoint since both occur if the outcome of the roll is a 1.
  • What about the probability of rolling a 1, 2, 3, 4, 5, or 6?
  • We are interested in the probability of rolling a 1, 4, or 5. ( a) Explain why the outcomes 1, 4, and 5 are disjoint.
  • These sets are commonly called events.
  • 2.8: (a) The random process is a die roll, and at most one of these outcomes can come up.

• Theoretical Probability

  • This means that in six out of every 10 times when the world is in its current state, it will rain.
  • For example, the probability of rolling any specific number on a six-sided die is one out of six: there are six, equally probable sides to land on, and each side is distinct from the others.
  • If the six on the die were changed to a one, you could logically conclude that the probability of rolling a one would be two out of six (or one out of three).
  • This is a theoretical probability; testing by rolling the die many times and recording the results would result in an experimental probability.
  • Each sequence is called a permutation (or ordering) of the five items.

• Homework

  • Suppose that you are offered the following "deal. " You roll a die.
  • If you roll a 6, you win $10.
  • If you roll a 4 or 5, you win $5.
  • What are you ultimately interested in here (the value of the roll or the money you win)?
  • Suppose that 20,000 married adults in the United States were randomly surveyed as to the number of children they have.