ST5214 Advanced Probability Theory (Sem 1:2009/10) References
... Probability: Theory and Examples by Durrett, Duxbury Press (main text) Convergence of Stochastic Processes by Pollard, Springer An Introduction to Probability Theory and its Applications by Feller, Wiley Probability and Measure by Billingsley, Wiley ...
... Probability: Theory and Examples by Durrett, Duxbury Press (main text) Convergence of Stochastic Processes by Pollard, Springer An Introduction to Probability Theory and its Applications by Feller, Wiley Probability and Measure by Billingsley, Wiley ...
3.2 Continuous Distributions
... example, http://integrals.wolfram.com/index.jsp. Use them to check your work but do not become dependent on them. 2. The probability distribution function evaluated at x ∈ R is not a probability. For example, ...
... example, http://integrals.wolfram.com/index.jsp. Use them to check your work but do not become dependent on them. 2. The probability distribution function evaluated at x ∈ R is not a probability. For example, ...
1999
... 5 A train goes from town A to town B in 9 hours. A second train goes from B to A in 6 hours. If the trains leave at the same time, go at a constant rate, and make no stops then how many hours after they leave will they meet? (a) 2.8 (b) 3.2 (c) 3.6 (d) 3.9 (e) 4.2 6. If x,y,z are positive numbers an ...
... 5 A train goes from town A to town B in 9 hours. A second train goes from B to A in 6 hours. If the trains leave at the same time, go at a constant rate, and make no stops then how many hours after they leave will they meet? (a) 2.8 (b) 3.2 (c) 3.6 (d) 3.9 (e) 4.2 6. If x,y,z are positive numbers an ...
Extra Topic: DISTRIBUTIONS OF FUNCTIONS OF RANDOM
... We can generalize this case when the transformation or mapping is one-to-one for discrete random variables. For a one-to-one transformation Y = g(X) for discrete X, the pmf of Y or fY (y) is obtained as, fY (y) = P (Y = y) = P (g(X) = y) = P (X = g −1(y)) = fX (g −1(y)). From the previous example w ...
... We can generalize this case when the transformation or mapping is one-to-one for discrete random variables. For a one-to-one transformation Y = g(X) for discrete X, the pmf of Y or fY (y) is obtained as, fY (y) = P (Y = y) = P (g(X) = y) = P (X = g −1(y)) = fX (g −1(y)). From the previous example w ...
4.1AB: Random Variables and Probability Distributions Objectives: 1
... 3. The length of time it takes to complete a test 4. The height of a tree at a nursery 5. The number of suitcases lost by an airline 6. The number of skittles in a bag 7. The weight of newborn babies ...
... 3. The length of time it takes to complete a test 4. The height of a tree at a nursery 5. The number of suitcases lost by an airline 6. The number of skittles in a bag 7. The weight of newborn babies ...
Calculator Notes for Chapter 4
... Calculator Note 4A: Generating Random Numbers You can generate random numbers using commands in the MATH menu. For example, to generate random integers between 0 and 99, press ç, arrow over to PRB, select 5:randInt(, and enter the expression randInt(0,99). Pressing Õ repeatedly generates more random ...
... Calculator Note 4A: Generating Random Numbers You can generate random numbers using commands in the MATH menu. For example, to generate random integers between 0 and 99, press ç, arrow over to PRB, select 5:randInt(, and enter the expression randInt(0,99). Pressing Õ repeatedly generates more random ...
Three Selection Algorithms Today we will look at three linear
... First let’s show that the expected number of comparisons used by this algorithm is 1.5n + o(n) in the case that it doesn’t give up and repeat. The two sorts of O(n3/4) elements, using our favorite deterministic O(n log n) algorithm, each take O(n3/4 log n) which is o(n). If we compare each element ...
... First let’s show that the expected number of comparisons used by this algorithm is 1.5n + o(n) in the case that it doesn’t give up and repeat. The two sorts of O(n3/4) elements, using our favorite deterministic O(n log n) algorithm, each take O(n3/4 log n) which is o(n). If we compare each element ...
Random Number Generation
... • addition modulo • addition of floating-point random numbers modulo 1 – x, y • Different random number sources ...
... • addition modulo • addition of floating-point random numbers modulo 1 – x, y • Different random number sources ...
Fisher–Yates shuffle
The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. A variant of the Fisher–Yates shuffle, known as Sattolo's algorithm, may be used to generate random cyclic permutations of length n instead. The Fisher–Yates shuffle is unbiased, so that every permutation is equally likely. The modern version of the algorithm is also rather efficient, requiring only time proportional to the number of items being shuffled and no additional storage space.Fisher–Yates shuffling is similar to randomly picking numbered tickets (combinatorics: distinguishable objects) out of a hat without replacement until there are none left.