Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
Let the random variable X have a discrete uniform distribution on the integers 0 ? x ? 99. Determine the mean and variance of X.

Applied Statistics and Probability for Engineers 6
Problem 77E Let the random variable X have a discrete uniform distribution on the integers 1 ? x ? 3. Determine the mean and variance of X.

Applied Statistics and Probability for Engineers 6
Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.

Applied Statistics and Probability for Engineers 6
Problem 79E Product codes of two, three, four, or five letters are equally likely. What are the mean and standard deviation of the number of letters in the codes?

Applied Statistics and Probability for Engineers 6
Problem 80E The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.0 and continuing through 590.9. Determine the mean and variance of the lengths.

Applied Statistics and Probability for Engineers 6
Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 675 to 700 nm. (a) What are the mean and variance of the wavelength distribution for this radiation? (b) If the wavelengths are uniformly distributed at i

Applied Statistics and Probability for Engineers 6
Problem 82E The probability of an operator entering alphanumeric data incorrectly into a field in a database is equally likely. The random variable X is the number of fields on a data entry form with 28 fields that have an error. Is X a discrete uniform random variable? Why or why not?

Applied Statistics and Probability for Engineers 6
Problem 83E Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.

Applied Statistics and Probability for Engineers 6
Problem 84E Show that for a discrete uniform random variable X, if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c2. That is, show that E (cX) = cE(X) and V (cX) = c2 V(X).

Applied Statistics and Probability for Engineers 6
Problem 85E The number of pages in a PDF document you create has a discrete uniform distribution from five to nine pages (including the end points). What are the mean and standard deviation of the number of pages in the document?

Applied Statistics and Probability for Engineers 6
Problem 86E Suppose that nine-digit Social Security numbers are assigned at random. If you randomly select a number, what is the probability that it belongs to one of the 300 million people in the United States?

Applied Statistics and Probability for Engineers 6
Problem 87E Suppose that 1000 seven-digit telephone numbers within your area code are dialed randomly. What is the probability that your number is called?

Applied Statistics and Probability for Engineers 6
The probability that data are entered incorrectly into a field in a database is 0.005. A data entry form has 28 fields, and errors occur independently for each field. The random variable X is the number of fields on the form with an error. Does X have a discrete uniform distribution? Why or why not?

Applied Statistics and Probability for Engineers 6
Each multiple-choice question on an exam has four choices. Suppose that there are 10 questions and the choice is selected randomly and independently for each question. Let X denote the number of questions answered correctly. Does X have a discrete uniform distribution? Why or why not?

Applied Statistics and Probability for Engineers 6
Consider the hospital data in Example 2-8. Suppose a patient is selected randomly from the collection in the table. Let X denote the hospital number of the selected patient (either 1, 2, 3, or 4). Does X have a discrete uniform distribution? Why or why not?