Applied Statistics and Probability for Engineers
5-9 The moments of a random variable can often be determined directly from the definition in Equation S5-7, but there is an alte ...
5-10 This last summation is the binomial expansion of [pet(1p)]n, so Taking the first and second derivatives, we obtain and If ...
5-11 Let. Then dx du, and this last expression above becomes Now the integral is just the total area under a standard normal d ...
5-12 Since the X’s are independent, and one may write For the case when the X’s are discrete, we would use the same approach rep ...
5-13 (a) Show that the moment generating function is (b) Use MX(t) to find the mean and variance of X. S5-16. The chi-squared ra ...
5-14 This result is interpreted as follows. The probability that a random variable differs from its mean by at least c standard ...
5-15 Thus, the probability that is within 3(0.01^2 n)^1 ^2 of is at least 89. Finally, nis chosen such that 3(0.01^2 n)^1 ...
189 6 Random Sampling and Data Description CHAPTER OUTLINE LEARNING OBJECTIVES After careful study of this chapter you should be ...
190 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION 6-1 DATA SUMMARY AND DISPLAY Well-constructed data summaries and displays are ...
6-1 DATA SUMMARY AND DISPLAY 191 hypothetical population,because it does not physically exist. Sometimes there is an actual phys ...
192 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION EXAMPLE 6-2 Table 6-1 displays the quantities needed for calculating the samp ...
numerical accuracy. A more efficient computational formula for the sample variance is obtained as follows: and since this last e ...
194 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION the squared deviations about the sample average must be used instead. However ...
6-2 RANDOM SAMPLING In most statistics problems, we work with a sample of observations selected from the popula- tion that we ar ...
196 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION chassis structural element to be normally distributed with mean and variance ...
6-3 STEM-AND-LEAF DIAGRAMS 197 We have encountered statistics before. For example, if is a random sample of size n, the sample m ...
198 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION Table 6-2 Compressive Strength (in psi) of 80 Aluminum-Lithium Alloy Specimen ...
6-3 STEM-AND-LEAF DIAGRAMS 199 Stem Leaf Frequency 76 1 87 1 97 1 10 5 1 2 11 5 8 0 3 12 1 0 3 3 13 4 1 3 5 3 5 6 14 2 9 5 8 3 1 ...
200 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION adequately displays the data. Figure 6-5(c) illustrates a stem-and-leaf displ ...
and ordered observations and interpolates as needed. For example, and Therefore, Minitab interpolates between the 20th and 21st ...
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