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Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable, hind the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.
13. Internet and Nobel Laureates Find the best predicted Nobel Laureate rate for Japan, which has 79.1 Internet users per 100 people. How does it compare to Japan’s Nobel Laureate rate of 1.5 per 10 million people?
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- A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward
- 3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage