GCSE higher probability
... lose the next 2? (Be careful!!) Sue counts cars outside her house one morning. The probability of seeing a red car was 0.2, the probability of seeing a black car was 0.3, the probability of seeing a silver car was 0.1 and the probability of seeing a blue car was 0.2. (a) What is the highest the prob ...
... lose the next 2? (Be careful!!) Sue counts cars outside her house one morning. The probability of seeing a red car was 0.2, the probability of seeing a black car was 0.3, the probability of seeing a silver car was 0.1 and the probability of seeing a blue car was 0.2. (a) What is the highest the prob ...
Representing a distribution by stopping a Brownian Motion: Root`s
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6 To show Eq. (5), observe that the variance of each individual
... where the arithmetic in the delta function is modulo 2. The delta function tells us that the tensor product over σx must only contain either 0 or 2 factors of σx only; all other terms have zero probability. Let’s separate out the case where there are no σx operators from when there are two. If there ...
... where the arithmetic in the delta function is modulo 2. The delta function tells us that the tensor product over σx must only contain either 0 or 2 factors of σx only; all other terms have zero probability. Let’s separate out the case where there are no σx operators from when there are two. If there ...
STAT 111 Recitation 1
... Two events D and E are mutually exclusive if they cannot both occur together. Then their intersection is the empty event and therefore, from the above equation, if D and E are mutually exclusive, Prob(D ∪ E ) = Prob(D) + Prob(E ). ...
... Two events D and E are mutually exclusive if they cannot both occur together. Then their intersection is the empty event and therefore, from the above equation, if D and E are mutually exclusive, Prob(D ∪ E ) = Prob(D) + Prob(E ). ...
Lecture 17
... data that he analyzed for regions of the Nile river which showed that Plots of log( RN / DN ) versus log N are linear with slope H 0.75. According to Feller’s analysis this must be an anomaly if the flows are i.i.d. with finite second moment. The basic problem raised by Hurst was to identify circu ...
... data that he analyzed for regions of the Nile river which showed that Plots of log( RN / DN ) versus log N are linear with slope H 0.75. According to Feller’s analysis this must be an anomaly if the flows are i.i.d. with finite second moment. The basic problem raised by Hurst was to identify circu ...
PROBABILITY I - UCLA Department of Mathematics
... this: A board is set up on the opposite side of the room, with different regions corresponding to different amounts of points. Darts are thrown across the room, and the number of points that you earn is equal to the number on the region the dart lands in. The math instructors want to play darts. As ...
... this: A board is set up on the opposite side of the room, with different regions corresponding to different amounts of points. Darts are thrown across the room, and the number of points that you earn is equal to the number on the region the dart lands in. The math instructors want to play darts. As ...
Sequences, Sums, Cardinality
... A recurrence relation for the sequence {an }n∈N is an equation that expresses an in terms of (one or more of) the previous elements a0 , a1 , . . . , an−1 of the sequence • Typically the recurrence relation expresses an in terms of just a fixed number of previous elements, e.g. an = g (an−1 , an−2 ) ...
... A recurrence relation for the sequence {an }n∈N is an equation that expresses an in terms of (one or more of) the previous elements a0 , a1 , . . . , an−1 of the sequence • Typically the recurrence relation expresses an in terms of just a fixed number of previous elements, e.g. an = g (an−1 , an−2 ) ...
BROWNIAN MOTION Definition 1. A standard Brownian (or a
... and let {Ft∗ }t ≥0 be the filtration of the process {W ∗ (t )}t ≥0 . Then (a) {W ∗ (t )}t ≥0 is a standard Brownian motion; and (b) For each t > 0, the σ−algebra Ft∗ is independent of Fτ . Details of the proof are omitted (see, for example, K ARATZAS & S HREVE, pp. 79ff). Let’s discuss briefly the m ...
... and let {Ft∗ }t ≥0 be the filtration of the process {W ∗ (t )}t ≥0 . Then (a) {W ∗ (t )}t ≥0 is a standard Brownian motion; and (b) For each t > 0, the σ−algebra Ft∗ is independent of Fτ . Details of the proof are omitted (see, for example, K ARATZAS & S HREVE, pp. 79ff). Let’s discuss briefly the m ...
key - BetsyMcCall.net
... If E & F are mutually exclusive, then p( E F ) P( E ) P( F ) 0.8 0.6 1.4 . This is not a possible probability value since it is larger than 1. Therefore, the intersection must be large enough to make this a possible value. Therefore, p( E F ) 0.4 . Likewise, the union of two events m ...
... If E & F are mutually exclusive, then p( E F ) P( E ) P( F ) 0.8 0.6 1.4 . This is not a possible probability value since it is larger than 1. Therefore, the intersection must be large enough to make this a possible value. Therefore, p( E F ) 0.4 . Likewise, the union of two events m ...
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.