All_Diff_ex_Feb29 (N-1) - University of Cincinnati
... Good. Now we focus on the probability that the Nth person coming in to such a party also had a different birthday from all other partygoers. Sure, we know that would be the chance of hitting any of the days not seen so far: Diff_Person = 365-(N-1) / 365 ...
... Good. Now we focus on the probability that the Nth person coming in to such a party also had a different birthday from all other partygoers. Sure, we know that would be the chance of hitting any of the days not seen so far: Diff_Person = 365-(N-1) / 365 ...
Conditional Probability and Independent Events
... Example 12: A certain loudspeaker system has four components: a woofer, a midrange, a tweeter, and an electrical crossover. It has been determined that on the average 1% of the woofers, 0.8% of the midranges, 0.5% of the tweeters, and 1.5% of the crossovers are defective. Determine the probability t ...
... Example 12: A certain loudspeaker system has four components: a woofer, a midrange, a tweeter, and an electrical crossover. It has been determined that on the average 1% of the woofers, 0.8% of the midranges, 0.5% of the tweeters, and 1.5% of the crossovers are defective. Determine the probability t ...
MOCK AMC 8 A - Art of Problem Solving
... the integer directly to its left or the integer directly to its right, with an equal probability of walking to either. After 6 minutes, what is the probablility that the dust particle returns to its starting point? (A) 5/32 ...
... the integer directly to its left or the integer directly to its right, with an equal probability of walking to either. After 6 minutes, what is the probablility that the dust particle returns to its starting point? (A) 5/32 ...
as a PDF
... Theorem 1, f˜ ◦ Fν ◦ α : (T, µ) → R has f˜ ◦ Fν ◦ α = f˜ = f , and similarly for Theorem 2. Consequently, we can replace ([0, 1], B, d x) by (T, µ) in Theorems 1 and 2, for any Borel space T with a continuous probability measure µ. The purpose of this note is to give an elementary proof of an extens ...
... Theorem 1, f˜ ◦ Fν ◦ α : (T, µ) → R has f˜ ◦ Fν ◦ α = f˜ = f , and similarly for Theorem 2. Consequently, we can replace ([0, 1], B, d x) by (T, µ) in Theorems 1 and 2, for any Borel space T with a continuous probability measure µ. The purpose of this note is to give an elementary proof of an extens ...
NCAAPMT Calculus Challenge Problem #9 Solutions Due February
... The figure at right illustrates the non-uniformity. The blue regions begin with a first non-zero digit of 1 and the red begin with 5. The areas of the two triangles below y = x are the same. If the ratio is less than one, then the first non-zero digits are uniformly distributed. However, if the rati ...
... The figure at right illustrates the non-uniformity. The blue regions begin with a first non-zero digit of 1 and the red begin with 5. The areas of the two triangles below y = x are the same. If the ratio is less than one, then the first non-zero digits are uniformly distributed. However, if the rati ...
11-2 Basic Probability
... is sometimes referred to as the Law of Large Numbers, which states that if an experiment is repeated a large number of times, the relative frequency of the outcome will tend to be close to the theoretical probability of the outcome. ...
... is sometimes referred to as the Law of Large Numbers, which states that if an experiment is repeated a large number of times, the relative frequency of the outcome will tend to be close to the theoretical probability of the outcome. ...
Means and Variances of Random Variables
... Mean of a Random Variable Example : Nelson is trying to get Homer to play a game of chance. This game costs $2 to play. The game is to flip a coin three times, and for each head that appears, Homer will win $1. Here is the probability distribution : Number of Heads Probability ...
... Mean of a Random Variable Example : Nelson is trying to get Homer to play a game of chance. This game costs $2 to play. The game is to flip a coin three times, and for each head that appears, Homer will win $1. Here is the probability distribution : Number of Heads Probability ...
Probability and Statistics 6th Grade
... Whinny for both. What portion of students did not receive a Whinny Award? Express your answer as a reduced fraction. 2. 2 points: A sock drawer contains 3 blue socks, 6 red socks, 7 yellow socks, and some number ...
... Whinny for both. What portion of students did not receive a Whinny Award? Express your answer as a reduced fraction. 2. 2 points: A sock drawer contains 3 blue socks, 6 red socks, 7 yellow socks, and some number ...
AP Stats Chap 5.1
... The myth of short-run regularity: The idea of probability is that randomness is predictable in the long run. Our intuition tries to tell us random phenomena should also be predictable in the short run. However, probability does not allow us to make short-run predictions. The myth of the “law of aver ...
... The myth of short-run regularity: The idea of probability is that randomness is predictable in the long run. Our intuition tries to tell us random phenomena should also be predictable in the short run. However, probability does not allow us to make short-run predictions. The myth of the “law of aver ...
22C:19 Discrete Math
... What is the probability that a family with two children has two boys, given that they have at least one boy? F = {BB, BG, GB} E = {BB} ...
... What is the probability that a family with two children has two boys, given that they have at least one boy? F = {BB, BG, GB} E = {BB} ...
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.