PowerPoint - Dr. Justin Bateh
... given. Actually, you should use this function to calculate different percentiles. In this problem one could ask what is the score of a student whose percentile is 90? This means approximately 90% of students scores are less than this number. On the other hand if we were asked to do this problem ...
... given. Actually, you should use this function to calculate different percentiles. In this problem one could ask what is the score of a student whose percentile is 90? This means approximately 90% of students scores are less than this number. On the other hand if we were asked to do this problem ...
Chapter 2 Functions and Graphs
... the independent variable t represents time, are often used to model population growth and radioactive decay. Note that if t = 0, then y = c. So, the constant c represents the initial population (or initial amount.) The constant k is called the relative growth rate. If the relative growth rate is ...
... the independent variable t represents time, are often used to model population growth and radioactive decay. Note that if t = 0, then y = c. So, the constant c represents the initial population (or initial amount.) The constant k is called the relative growth rate. If the relative growth rate is ...
Document
... Solution: Population is Exponential(=5) a) =5 b) P(X > 12) = e-12/ = e-12/(5) =e-2.4 = 0.090718 b) P(X < x ) = 0.95 1-e- (x/ 5) =0.95 x =-5*ln(1-0.95) = 14.9787 hours 2. PVC pipes are manufactured with a mean diameter of 1.01 inch and standard deviation 0.03 inch. A pipe with diameter less th ...
... Solution: Population is Exponential(=5) a) =5 b) P(X > 12) = e-12/ = e-12/(5) =e-2.4 = 0.090718 b) P(X < x ) = 0.95 1-e- (x/ 5) =0.95 x =-5*ln(1-0.95) = 14.9787 hours 2. PVC pipes are manufactured with a mean diameter of 1.01 inch and standard deviation 0.03 inch. A pipe with diameter less th ...
Chapter 3 More about Discrete Random Variables
... • To transmit message i using an optical communication system. • When light of intensity λi strikes the photodetector, the number of photoelectrons generated is a Poisson(λi ) random variable. • Find the conditional probability that the number of photoelectrons observed at the photodetector is less ...
... • To transmit message i using an optical communication system. • When light of intensity λi strikes the photodetector, the number of photoelectrons generated is a Poisson(λi ) random variable. • Find the conditional probability that the number of photoelectrons observed at the photodetector is less ...
Design of Algorithms - Homework II (Solutions)
... That is, Xij is the indicator random variable for the event that the pair (i, j), with i < j, is inverted. Now, Pr{Xij = 1} is equal to 12 , because in any random permutation of distinct numbers, there are precisely two possibilities, viz., A[i] > A[j] and A[j] > A[i], with each of them having proba ...
... That is, Xij is the indicator random variable for the event that the pair (i, j), with i < j, is inverted. Now, Pr{Xij = 1} is equal to 12 , because in any random permutation of distinct numbers, there are precisely two possibilities, viz., A[i] > A[j] and A[j] > A[i], with each of them having proba ...
Community detection via random walk
... If two vertices i, j are in the same community, the probability then Pt (i, j) will surely be high. But the fact that Pt (i, j) is high does not necessarily imply that i, j are in the same community. ...
... If two vertices i, j are in the same community, the probability then Pt (i, j) will surely be high. But the fact that Pt (i, j) is high does not necessarily imply that i, j are in the same community. ...
Simulated annealing
Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more efficient than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution.The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. Both are attributes of the material that depend on its thermodynamic free energy. Heating and cooling the material affects both the temperature and the thermodynamic free energy. While the same amount of cooling brings the same amount of decrease in temperature it will bring a bigger or smaller decrease in the thermodynamic free energy depending on the rate that it occurs, with a slower rate producing a bigger decrease.This notion of slow cooling is implemented in the Simulated Annealing algorithm as a slow decrease in the probability of accepting worse solutions as it explores the solution space. Accepting worse solutions is a fundamental property of metaheuristics because it allows for a more extensive search for the optimal solution.The method was independently described by Scott Kirkpatrick, C. Daniel Gelatt and Mario P. Vecchi in 1983, and by Vlado Černý in 1985. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by M.N. Rosenbluth and published in a paper by N. Metropolis et al. in 1953.