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Pair wise independence does not imply mutual independence. Assume that the particular scales used in dry-batching a concrete mix are such that both aggregate and cement weights are subject to error. The two weights are measured independently. The aggregate is equally likely to be measured exactly correct or 20 pounds too large. The cement is equally likely to be measured exactly correct or 20 pounds too small. The total weight of aggregate and cement is desired. Let event A be no error in aggregate weight measurement, event B be no error in cement weight, and event C be no error in total weight.
(a) Show that the pairs of events A and B, A and C, and B and C are independent.
(b) Use (a) as a counterexample to show that pairwise independence does not imply mutual independence.
(c) Is the inverse statement true?
What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean = 935?
Compare to a surface emission aperture with the same width, but a length of 35 µm. Which one do you expect to have less divergence and what is the beam shape in each case?
Manufacturer of mole and gopher poison has experienced the following monthly demand for an environmentally sound pesticide poison. Using a Average method, what would the forecast have been for July?
Bismuth (a) and cadmium (b) form a eutectic at 144°C and xa 5 0.45. They are also completely immiscible in the solid phase. The melting points for bismuth and cadmium are 271°C and 321°C, respectively. The enthalpies of fusion of these elements a..
Write an appropriate null hypothesis for this analysis. What is the mean weight of the girls before and after treatment? What is the standard deviation of the weight measurements before and after treatment
Women have been on a diet within the past 12 months. Using Normal approximation, what is the probability (±0.001) that 76% or more of the women in the sample have been on a diet?
How do you derive the OLS estimator for a regression model with one explanatory variable and an intercept?
Explain what synthetic division is. Illustrate with example. In synthetic division, what relationship does the divisor and remainder have to the original polynomial function, according to the Remainder Theorem?
Consider the following two-way frequency table with three populations and three values of a categorical variable.
a research report concludes that there are significant differences among treatments with f227 8.62 p lt .01. if the
Two pain relief drugs are being considered. A random sample of 6 doses of the first drug showed that the average amount of time required before the drug was absorbed into the bloodstream was ??
Define a token class Almost Reserved to be those identifiers that are not reserved words but that would be if a single character were changed. Why is it useful to know that an identifier is "almost" a reserved word?
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