MATHEMATICS SS3 HOLIDAY SCHEME
... -It is assumed that when children are born they are equally likely to be boys or girls. What is the probability that a family of four children contains a. three boys and one girl b. two boys and two girls -The 18 TH term of an arithmetic progression 25. Find its first term if its common difference i ...
... -It is assumed that when children are born they are equally likely to be boys or girls. What is the probability that a family of four children contains a. three boys and one girl b. two boys and two girls -The 18 TH term of an arithmetic progression 25. Find its first term if its common difference i ...
Philosophy of Science, 69 (September 2002) pp
... particular, Skyrms (1997) both reviews and discusses the utility of martingale arguments in establishing the convergence of beliefs within the context of radical probabilism. The classical martingale converence theorem, however, assumes the countable additivity of the underlying probability measure; ...
... particular, Skyrms (1997) both reviews and discusses the utility of martingale arguments in establishing the convergence of beliefs within the context of radical probabilism. The classical martingale converence theorem, however, assumes the countable additivity of the underlying probability measure; ...
f7ch6
... the probability that he misses is q, where q = 1 – p. Write an expression for the probability that, in 10 shots, he hits the target 6 times. If the probability that an experiment results in a successful outcome is p and the probability that the outcome is a failure is q, where q = 1 – p, and if X is ...
... the probability that he misses is q, where q = 1 – p. Write an expression for the probability that, in 10 shots, he hits the target 6 times. If the probability that an experiment results in a successful outcome is p and the probability that the outcome is a failure is q, where q = 1 – p, and if X is ...
Lecture 1
... • Associative laws: (E ∪ F ) ∪ G = E ∪ (F ∪ G), (E ∩ F ) ∩ G = E ∩ (F ∩ G) • Distributive laws: (E ∪ F ) ∩ G = (E ∩ G) ∪ (F ∩ G), (E ∩ F ) ∪ G = (E ∪ G) ∩ (F ∪ G) DeMorgan’s laws: n ...
... • Associative laws: (E ∪ F ) ∪ G = E ∪ (F ∪ G), (E ∩ F ) ∩ G = E ∩ (F ∩ G) • Distributive laws: (E ∪ F ) ∩ G = (E ∩ G) ∪ (F ∩ G), (E ∩ F ) ∪ G = (E ∪ G) ∩ (F ∪ G) DeMorgan’s laws: n ...
Solution Week 38 (6/2/03) Sum over 1 (a) First Solution: We will use
... that their sum does not exceed s equals sn /n! (for all s ≤ 1). Proof: Assume inductively that the result holds for a given n. (It clearly holds for all s ≤ 1 when n = 1.) What is the probability that n + 1 numbers sum to no more than t (with t ≤ 1)? Let the (n + 1)st number have the value x. Then t ...
... that their sum does not exceed s equals sn /n! (for all s ≤ 1). Proof: Assume inductively that the result holds for a given n. (It clearly holds for all s ≤ 1 when n = 1.) What is the probability that n + 1 numbers sum to no more than t (with t ≤ 1)? Let the (n + 1)st number have the value x. Then t ...
Lecture 8 Generating a non-uniform probability distribution Discrete
... discrete case, the probability for any particular outcome is a unitless number between 0 and 1. Many outcomes are however, continuous. Examples of continuous outcomes include: a particle’s position, momentum, energy, cross section, to name a few. Suppose the continuous outcome is the quantity x. The ...
... discrete case, the probability for any particular outcome is a unitless number between 0 and 1. Many outcomes are however, continuous. Examples of continuous outcomes include: a particle’s position, momentum, energy, cross section, to name a few. Suppose the continuous outcome is the quantity x. The ...
Document
... The probability distribution for a random variable describes how probabilities are distributed over the values of the random variable. The probability distribution is defined by a probability function, denoted by f(x), which provides the probability for each value of the random variable. The require ...
... The probability distribution for a random variable describes how probabilities are distributed over the values of the random variable. The probability distribution is defined by a probability function, denoted by f(x), which provides the probability for each value of the random variable. The require ...
Probability
... If X is distribution in this way, we write X Bin(n,p) where n is the number of independent trials and p is the probability of a successful outcome in one trial n and p are called the parameters of the distribution. Sometimes, we will use b(x; n,p) to represent the probability function when XBin(n ...
... If X is distribution in this way, we write X Bin(n,p) where n is the number of independent trials and p is the probability of a successful outcome in one trial n and p are called the parameters of the distribution. Sometimes, we will use b(x; n,p) to represent the probability function when XBin(n ...
Quiz 8 - Cypress HS
... (e) All of these 10. A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let X be the number of cards you turn over until you observe the first red card. The random variable X has which of ...
... (e) All of these 10. A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let X be the number of cards you turn over until you observe the first red card. The random variable X has which of ...
5.1.1 The Idea of Probability Chance behavior is unpredictable in
... How do insurance companies decide how much to charge for life insurance? We can’t predict whether a particular person will die in the next year. But the National Center for Health Statistics says that ...
... How do insurance companies decide how much to charge for life insurance? We can’t predict whether a particular person will die in the next year. But the National Center for Health Statistics says that ...
Document
... Discrete random variable: either a finite number of values or countable number of values, where “countable” refers to the fact that there might be infinitely many values, but they result from a counting process. (it cannot be a decimal) Continuous random variable: infinitely many values, and those v ...
... Discrete random variable: either a finite number of values or countable number of values, where “countable” refers to the fact that there might be infinitely many values, but they result from a counting process. (it cannot be a decimal) Continuous random variable: infinitely many values, and those v ...
7.SP.6_11_28_12_formatted
... other groups, or increase the number of trials in a simulation to look at the long-run relative frequencies. Example: Each group receives a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles. Each group performs 50 pulls, recording the color of marble drawn and replacing the mar ...
... other groups, or increase the number of trials in a simulation to look at the long-run relative frequencies. Example: Each group receives a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles. Each group performs 50 pulls, recording the color of marble drawn and replacing the mar ...
Lecture5_SP17_probability_history_solutions
... brought to Europe by soldiers returning from the Crusades, Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in ...
... brought to Europe by soldiers returning from the Crusades, Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.