The Chemistry Maths Book, Second Edition

590 Chapter 20Numerical methods EXAMPLE 20.19Apply the Runge–Kutta methods of orders 2 and 4 to the initial value problem in Exa ...

20.10 Systems of differential equations 591 general problem is that of Nfirst-order initial value problems for Nfunctions,y 1 (x ...

592 Chapter 20Numerical methods which can be interpreted as first-order rate processes with rate constants 1 and 100. Stiff prob ...

20.11 Exercises 593 16.Use linear interpolation to computef(0.04), f(0.26), f(0.5), f(0.81). 17.Use quadratic interpolation to c ...

594 Chapter 20Numerical methods (i) Use Gauss elimination to find the value of λfor which the following equations have a solut ...

21 Probability and statistics 21.1 Concepts The practice of statistics, the collection and statistical analysis of data, has bec ...

596 Chapter 21Probability and statistics Table 21.1 50 experimental values 4673635766 3445865265 7744308544 6282765554 952293657 ...

21.2 Descriptive statistics 597 the heights (in appropriate units) of a sample of the population, the weights of a sample of man ...

598 Chapter 21Probability and statistics measurements of a physical quantity have random errors, with positive and negative erro ...

21.2 Descriptive statistics 599 in which the sum is over the kdistinct values (or classes). Other measures of average, seldom us ...

600 Chapter 21Probability and statistics Qualitative measures of spread are the range, the difference between the extreme data v ...

21.3 Frequency and probability 601 The variance (21.5) can be written in simpler form as ‘the mean of the squares minus the squa ...

602 Chapter 21Probability and statistics Table 21.4 Nn(H) f(H) 256 118 0.461 4040 2068 0.512 12000 6062 0.505 24000 11942 0.498 ...

21.4 Combinations of probabilities 603 The variance Vand standard deviation σof the probability distribution (of the population) ...

604 Chapter 21Probability and statistics Independent events The possible outcomes of tossing a coin twice are {HH, HT, TH, TT}, ...

21.5 The binomial distribution 605 equal probabilities:. The 4 possible outcomes of 2 tosses are HH, HT, TH, and TT, each with p ...

606 Chapter 21Probability and statistics More generally, the binomial distribution applies to any experiment whose outcomes can ...

21.6 Permutations and combinations 607 Multinomial distributions Multinomial distributions are generalizations of the binomial d ...

608 Chapter 21Probability and statistics objects can therefore be arranged inn(n 1 − 1 1)ways. The third object can occupyn 1 − ...

21.6 Permutations and combinations 609 The number of combinations of nobjects taken rat a time is the same as the number of ways ...