Fundamentals of Probability and Statistics for Engineers

function BINOMDIST in Microsoft ExcelTM2000 gives individual binomial probabilities given by Equation (6.2). Other statistical f ...

The moments and distribution of X can be easily found by using Equation (6.10). Since it follows from Equation (4.38) that which ...

it be given that, on average, a telephone user is on the phone 5 minutes per hour; an estimate of p is The solution to this prob ...

Answer: for k min (n 1 , m), we have where we have used the result given in Example 6.3 that X Y is binomially distributed with ...

The corresponding probability distribution function is where m is the largest integer less than or equal to x. The mean and vari ...

which may seem much smaller than what we experience in similar situa- tions. Example 6.6.Problem: assume that the probability of ...

and P(B) is simply Substituting Equations (6.19) and (6.20) into Equation (6.18) results in We note that, as expected, it reduce ...

which is the reason for the name ‘negative binomial distribution’. The mean and variance of random variable X can be determined ...

Example 6.9.The negative binomial distribution is widely used in waiting- time problems. Consider, for example, a car waiting on ...

The formula given by Equation (6.30) is an important higher-dimensional joint probability distribution. It is called the multino ...

To fix ideas in the following development, let us consider the problem of passenger arrivals at a bus terminal during a specifie ...

It follows from Equations (6.34) and (6.36) that In order to determine probability mass function based on the assumptions stated ...

Substituting Equations (6.34), (6.37), and (6.40) into Equation (6.41) and letting we obtain which yields Continuing in this way ...

where m is the observed number of arrivals in n unit time intervals. Similarly, since represents the average number of arrivals ...

a random manner both in space (amplitude and velocity) and in time (arrival rate). Considering the time aspect alone, observatio ...

0.999990.9999 0.9990.99 0.90.8 0.8 0.70.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.01 0.001 0.00010.00001 1.0 2 3 4 5 6 7 7 ...

the PDF associated with a Poisson–distributed random variable. The answer to Example 6.11, for example, can easily be read off f ...

Answer: let X be the number of eggs laid by the insect, and Y be the number of eggs developed. Then, given X r, the distribution ...

volumes, and if it is reasonable to assume that the probability of finding k flaws in any region depends only on the volume and ...

This Poisson approximation to the binomial distribution can be used to advan- tage from the point of view of computational labor ...