Found inside – Page 24observing any value or set of values of the variable can be known, ... A discrete random variable is one that can take on only a finite (or at most ... Found inside – Page 2A deterministic variable is one whose value can be calculated or determined ... This means that the instantaneous value for a random variable can only be ... Found inside – Page 212... distributed random variables ( a variable that can only take on one of two ... central limit theorem may be stated as : the distribution of mean values ... Found inside – Page 159So, if we toss a single coin there is the probability of 0.5 that it will come down ... outcome generates one, and only one, value of the random variable. Found inside – Page 21Hence , the numbers 1 , 2 , . . . 6 , are the values of the random variables . This example should not lead one to believe that a random variable can only be obtained from experimentation . In fact any function of a random variable is also a ... This text is intended for a one-semester course, and offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Found inside – Page 89This is because the frequency definition can only describe the probability of a random variable: a quantity that can meaningfully be considered to take on ... Found inside – Page 38The only possible value for X being the mean value X we have p ( x ) = 6 ( x - 7 ) It can happen , for example , as in the ... p ( x ; ty ) - 0 [ x - XXtz7 ] 1 It can also happen that X is normally a random variable but in the limit can only take one value . Found inside – Page 66Type Uniform distribution Acceptable Mean Standard ( Standard Value deviation over deviation / mean | 20 simulations ... is suitable for modeling uncertainty in a variable , when one can only estimate lower and upper limits for the variable . ... of ignorance , the uniform probability distribution is often used to express one ' s ignorance about a random variable . The Beta distribution is suitable when one can estimate the most probable value of a variable besides its lower and upper limit . Found inside – Page 215The variables in the mathematical model will be either deterministic or random . A deterministic variable can take on only one value ; a random variable can ... Found inside – Page 105A random variable can take on many possible values from the D, but only one ... every connection has the same chance to be selected) could be any one of the ... Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. * Exceptional exposition and numerous ... Found inside – Page 110In a probability mass function ( discrete distribution ) , the random variable is allowed to take on only selected values ( for ... The random variable , number of successes , can only take on zero and positive integer values from one to n ( the ... Found inside – Page 50ID Height Weight Blood pressure Pulse rate Random variable 40 random ... values that could fill one cell is different across the possible values that ... Found inside – Page 41The observed value of X must be 1, 2, 3, 4, 5 or 6. 2. On a given roll the random variable X can only take one of those values. Found inside – Page 88In both examples we are interested in a numerical value of an object selected at random. These numerical values are ... These two random variables differ in one important respect. The measurement of salt can ... If a variable can assume only a finite number of values or whole number values, it is discrete. (See Figure 4-6.) ... Found inside – Page 17-105There are two types of random variables , discrete and continuous . A discrete random variable is one that can only take on values that are whole numbers . Found inside – Page 196... is clearly non-negative and it should be stressed that in general E[g(X)] at g[E(X)] and in particular E(Xz) ¢E2 (X), unless X can only assume one value ... Found inside – Page 646Then, X is not associated with any particular value, but we know X will take ... A random variable that can only take on the values zero and one is called a ... .Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Found inside – Page 1554 : Two random variables X and Y are linearly dependent if Y can be written in the form maanis00 Y = ax + b lincar ... Since random variables which assume only one value with nonzero probability are of little interest , linear dependence ... Found inside – Page 2572.1 Random Variables An intuitive definition of a random variable is that it ... In other words, each event in the sample space can only take on one value ... Found insideThe book also provides worked out examples and solved problems for a wide variety of transportation engineering challenges. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education. Found inside – Page 16In Example 2.11 the random variable can assume continuous values. a. Discrete Random Variables A random variable that can only assume discrete values is ... Found inside – Page 39A random variable is often defined as a variable whose value is a number determined by ... variable is one that can only assume a limited number of values . Found inside – Page 8We shall usually use a single capital letter, such as X , to denote a random variable with the corresponding small letter, x, being used to ... Furthermore, the random variable X has only eleven possible values, x = 2, 3, ... , 12, while the sample space contains 36 points. ... Actually continuous random variables have many nice properties, and complicated discrete variables can frequently be approximated by ... Found inside – Page 363... two random variables X and X , are uncorrelated if and only if their correlation coefficient is zero . The correlation coefficient provides a measure of how good a prediction of the value of one of the random variables can be formed on the basis ... Found inside – Page 21A quantity x that can be determined quantitatively and that in successive but similar ... A discrete random variable takes one of a set of discrete values. Found inside – Page 112No two bolts may be exactly the same length , but our measuring devices can only measure to a certain accuracy and therefore all the ... Generally it is more convenient to use a continuous model when the variable can take on any one of a large number of possible values and the ... This function gives the probability that a random variable will have a value less than or equal to some specific number X * . Found inside – Page 20INTRODUCTION A stochastic process is a sequence of random variables , The index of the sequence is called the parameter of the process ... It or can be discrete , in which case the process will be designated { xm , } { x ( t ) } continuous , The value of the random variable is called the state of the process . ... With an ordinary random variable , one can only average in one direction , across the population . Found inside – Page 355A dichotomous random variable is simply a random variable that can only assume one of two values . For example , a simple Bernoulli trial is an example of a ... Found inside – Page 16Define the covariance and correlation between two random variables, ... occurs when a random variable can only be one of two possible values—for example, ... Found inside – Page 283In the absence of known component random variable distributions , the mean and variance can be estimated from n ... Consequently one can only generate single values of the function , and the derivatives must be evaluated numerically in a ... "This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students. Found inside – Page 225Let Y ( x ) be the distribution function of a variable X which can only have one value , 0 , for the sake of simplicity , with the ... express the distribution function of a random variable which has the values xi , X2 , . . . , with the probabilities P1 , P2 , . Found inside – Page 261One cannot say with certainty Surprises what the value of a random variable will be but only the Water resources managers may also want to consider how likelihood or probability that it will be within some specvulnerable a system is to ... Found inside – Page 184These random variables can take on any value in an interval of real numbers . That is not to say that every value in the interval can be found in sample data if one looks long enough ; one may never observe a patient weighing exactly 172 . Found inside – Page 332Since the countable variable can only have certain values and not all values ... the number of sixes in two rolls of a dice can only be zero, one or two and ... Found inside – Page 5-13Types of Random Variable: Random variable may be discrete or continuous. Discrete Random Variable: A variable can take one value from a discrete set of ... Found inside – Page 295THE CONCEPT OF PROBABILITY A random variable may be called a probability variable . Although we can assign values to a systematic variable with certainty ( each “ event ” has only one value ) , the values of the random variable are ... Found inside – Page 1181 Discrete Random Variables As we noted in Chapter 1 , the experimental events of greatest interest are often numerical , i . e . , we conduct an ... 2 A discrete random variable Y is one that can assume only a countable number of values . 4 . Found insideThe book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional Found inside – Page 297However , how accurate will we be on this one occasion ? We may only have one random sample , have determined one sample mean T , and hope that this one value lies close to the population mean . We know that as a random variable , X ... Found inside – Page 197E. C. the annual rainfall in a city A discrete random variable is one that can take on only values that are integers (positive and negative whole numbers ... Found inside – Page 1315... distribution have little interest in the more general case . 2 . Complete mutual dependence of random variables . A random variable Y will be said to be completely dependent on a random variable X if Y takes only one value for each value of ... Written by three of the world’s most renowned petroleum and environmental engineers, Probability in Petroleum and Environmental Engineering is the first book to offer the practicing engineer and engineering student new cutting-edge ... Found inside – Page 163A stochastic process is one which changes over time in an uncertain way. A discrete stochastic process for a variable is one where the variable can only ... Found insideThe text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level. Found inside – Page 341Two sets of observed values of x are available : for every patient we have one value before and one value after the ... If x is assumed to have the same distribution for every patient , a two sample test can be applied , but this condition is ... Let x ; ( i = 1 , ... , n ) be the random variable x for the įth patient before the treatment and x ; the corresponding variable after . ... This assumption is inevitable , if the influence of the drug only is to be ascertained . where the z ; are any given numbers ... One to believe that a random variable Y is one that can only..., across the population can estimate the most probable value of X must be 1, 2, we... 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