introduction to this chapter

... back at least to 1754, when Casanova, writing in his memoirs, History of My Life, writes She [Casanova’s mistress] made me promise to go to the casino [the Ridotto in Venice] for money to play in ... applied to human affairs.9 Exercises Modify the program CoinTosses to toss a coin n times and print out after every 100 tosses the proportion of heads minus 1/2 Do these numbers appear to approach ... first time it comes up heads If this occurs on the jth toss you are paid 2j dollars You are sure to win at least dollars so you should be willing to pay to play this game—but how much? Few people...

Ngày tải lên: 04/07/2014, 10:20

... with careful planning one would have to be extremely lucky to be able to stop so cleverly The second author likes to trace his interest in probability theory to the Chicago World’s Fair of 1933 ... referring to a continuous random variable X (say with a uniform density function), it is customary to say that “X is uniformly distributed on the interval [a, b].” It is also customary to refer to the ... need to refer to such a function We will call this function rnd Monte Carlo Procedure and Areas It is sometimes desirable to estimate quantities whose exact values are difficult or impossible to...

Ngày tải lên: 04/07/2014, 10:20

... went to a2 , a2 to a1 , a3 to a4 , and a4 to a3 If we always choose the top row to be then, to prescribe the permutation, we need only give the bottom row, with the understanding that this tells ... factors Either n! + is prime or it has a proper factor In the latter case, this factor cannot divide n! and hence must be between n and n! + If this factor is not prime, then it has a factor ... it, the numerator of the 122 CHAPTER COMBINATORICS corresponding factor in the probability is i, and the number of cards in this stack decreases by Thus, the numerator is seen to be k!(n − k)!,...

Ngày tải lên: 04/07/2014, 10:20

... Baba know that I am going to give then either an envelope with $5 or one with $10 and I am going to toss a coin to decide which to give to Ali, and then give the other to Baba Then Ali can argue ... the first toss of a coin to change the probability that you would assign to the possible outcomes of the second toss, that is, you would not expect that the second toss depends on the first This idea ... and, if offered a chance to switch to another door, takes the offer Now suppose that a contestant decides in advance to play the “stay” strategy His only action in this case is to pick a door (and...

Ngày tải lên: 04/07/2014, 10:20

... appears to grow without limit We can now ask: How long will a customer have to wait in the queue for service? To examine this question, we let Wi be the length of time that the ith customer has to ... has this blood type (b) How many people would have to be tested to give a probability greater than 1/2 of finding at least one person with this blood type? 15 Write a program for the user to input ... of this problem is to check the hypothesis that the chosen numbers are uniformly distributed To this, compute the value v of the random variable χ2 given in Example 5.10 In the present case, this...

Ngày tải lên: 04/07/2014, 10:20

... buys the stock on the first day at its price V He then waits until the price of the stock increases by one to V + and sells He then continues to watch the stock until its price falls back to V He ... holds the stock, it does not get back up to V + 1; and this is the only we he can lose In Figure 6.4 we illustrate a typical history if Mr Ace must stop in twenty days Mr Ace holds the stock under ... fair coin is tossed three times It is natural to think of X as the sum of the random variables X1 , X2 , X3 , where Xi is defined to be if the ith toss comes up heads, and if the ith toss comes...

Ngày tải lên: 04/07/2014, 10:20

... · = , = 36 36 216 = and so forth This is clearly a tedious job, and a program should be written to carry out this calculation To this we first write a program to form the convolution of two densities ... that this provides a practical way to estimate the value of µ 13 Particles are subject to collisions that cause them to split into two parts with each part a fraction of the parent Suppose that this ... than this, taking into account voids in suits, and so forth, but we consider here this simplified form of the point count.) If a card is dealt at random to a player, then the point count for this...

Ngày tải lên: 04/07/2014, 10:20

... the remaining chapters of this thesis.6 Bernoulli concludes his long proof with the remark: Whence, finally, this one thing seems to follow: that if observations of all events were to be continued ... fate I now know whether Plato wished to aim at this in his doctrine of the universal return of things, according to which he predicted that all things will return to their original state after ... and according to a constant law of alternation, so that even in the most accidental and fortuitous occurrences we would be bound to recognize, as it were, a certain necessity and, so to speak, a...

Ngày tải lên: 04/07/2014, 10:20

... does not seem to increase or decrease from one 9.2 DISCRETE INDEPENDENT TRIALS 349 generation to the next This was known at the time of Galton, and his attempts to explain this led him to the idea ... expanded into a Series, from whence are deduced some practical Rules to estimate the Degree of Assent which is to be given to Experiments.3 De Moivre’s proof used the approximation to factorials ... actual answer in this case, to five places, is 99821 It is important to work a few problems by hand to understand the conversion from a given inequality to an inequality relating to the standardized...

Ngày tải lên: 04/07/2014, 10:20

... One solution of this equation is always d = 1, since = p0 + p1 + p2 + · · · This is where Watson made his mistake He assumed that was the only solution to Equation 10.3 To examine this question ... solution The other is found to be 1−b−c d= c(1 − c) z =1− It is easy to verify that d < just when m > It is possible in this case to find the distribution of Zn This is done by first finding the ... geometric model tends to favor the larger numbers of offspring but is similar enough to show that this modified geometric distribution might be appropriate to use for studies of this kind Recall that...

Ngày tải lên: 04/07/2014, 10:20

... vector whose jth component is the number of entries to the jth compartment: x = (2 3 2) It is easy to check that this vector is indeed a fixed vector so that the unique probability vector is this ... to understand if one imagines making the array into a cylinder by gluing the top and bottom edge together, and then making the cylinder into a doughnut by gluing the two circular boundaries together.) ... as n goes to ∞ But by similar reasoning to that used above, the difference between this last expression and P (Xn = j) goes to as n goes to ∞ Therefore, P (Xn = j) → wj , as n goes to ∞ This completes...

Ngày tải lên: 04/07/2014, 10:20

... into n sets, depending upon the time of the first return to the origin A path in this collection which has a first return to the origin at time 2k consists of an initial segment from (0, 0) to ... noted that this series converges for x ∈ (−1, 1) In fact, it is possible to show that this series also converges for x = ±1 by using Exercise 4, together with the fact that f2m = u2m 2m − (This fact ... 12.5 gives rise to the sum m 22m f2k k=1 From Exercise 2, we see that this sum is just (1 − u2m )22m Thus, we need to create a generating function whose mth coefficient is this term; this generating...

Ngày tải lên: 04/07/2014, 10:20

... Lecture Notes: Introduction to Finite Element Method Chapter Introduction Row and Column Vectors v = [1 v v2 v3 ]  w1    w = w  w   3 Matrix ... system of equations is to found the inverse of the coefficient matrix © 1998 Yijun Liu, University of Cincinnati 11 Lecture Notes: Introduction to Finite Element Method Chapter Introduction Solution ... ad − bc c d  © 1998 Yijun Liu, University of Cincinnati Lecture Notes: Introduction to Finite Element Method Chapter Introduction and a11 a12 det a21 a22   a31 a32 a13  a23  = a11a22a33...

Ngày tải lên: 17/10/2013, 11:15

... simple To add a breakpoint, move the cursor to the line where we want to set a breakpoint The command to enable a breakpoint can be given from the Toggle Breakpoint hot button on the project toolbar ... the integrator output voltage to get back to zero is directly proportional to the input voltage This technique is very precise and can produce ADCs with high resolution Since the integrator is used ... testing DSP code Software simulators run on a host computer to mimic the behavior of a DSP chip The 18 INTRODUCTION TO REAL-TIME DIGITAL SIGNAL PROCESSING simulator is able to show memory contents,...

Ngày tải lên: 17/10/2013, 14:15

Ngày tải lên: 17/10/2013, 19:15

... link time This maximizes performance by enabling the programmer to link the code and data objects into specific memory locations The archiver allows users to collect a group of files into a single ... data that can be loaded into memory space Assembler directives are used to control the assembly process and to enter data into the program Assembly directives can be used to initialize memory, define ... breakpoints to be set at a particular point in a program to examine the registers and the memory locations in order to evaluate the real-time results using a DSP board Emulators allow the DSP software to...

Ngày tải lên: 19/10/2013, 23:15

Ngày tải lên: 07/11/2013, 09:15

... enabled,history size is 10 (略) Router#terminal history size ? Size of history buffer Router#terminal history size 25 Router#sh terminal (略) History is enabled,history size is 25 (略) Gather Basic Routing ... 1.show history:显示最后输入的 10 条命令,默认是 10 条,可以修改该值 2.terminal history size:修改显示最后输入过的的命令的数量,默认是 10 条,最大是 256 条 3.show terminal:显示命令历史缓存大小,如下: Router#sh terminal (略) History is enabled,history size ... connector Bring Up an Interface 打开和关闭 个接口,分别使用 shutdown 和 no shutdown 命令,当你关闭某个接口的时候,使用 sh interfaces 命令可以查看接口状态,并且你将看到以下输出: Router#sh int e0 Ethernet0 is administratively down,line protocol...

Ngày tải lên: 10/12/2013, 16:15

Ngày tải lên: 14/12/2013, 12:15

Ngày tải lên: 14/12/2013, 12:15