Let X be a continuous rv with the following cdf.F(x) =1+ In0 < x < 71X > 7[This type of cdf is suggested in the article "Variability in Measured Bedload-Transport Rates"† as a model for a certain hydrologic variable.](a) What is P(X < 5)? (Round your answer to three decimal places.)(b) What is P(5 < X < 6)? (Round your answer to three decimal places.)(c) What is the pdf of X?

Answered: Image /qna-images/answer/f1be90e7-dd06-4cff-990d-d77cf8d4fe33.jpg

Answered: F(x) = + In 0 < xs7 x > 7 [This type of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. You estimated a regression with the following output. Source | SS df MS Number of obs = 210 -------------+---------------------------------- F(1, 208) = 940.28 Model | 5529353.01 1 5529353.01 Prob > F = 0.0000 Residual | 1223155.7 208 5880.55624 R-squared = 0.8189 -------------+---------------------------------- Adj R-squared = 0.8180 Total | 6752508.71 209 32308.6541 Root MSE = 76.685 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 13.66711 .4457062 30.66 0.000 12.78843 14.54579 _cons | 103.7139 41.86814 2.48 0.014 21.17362 186.2542…
Q1: The data points below are related to a chemi-thermo-mechanical pulp from mixed density hardwoods. They relate Y (specific surface area of the fibres in cm/g) to the % NaOH (sodium hydroxide) used as a pretreatment chemical and the treatment time (min) for different batches of pulp. The variables are present at three different levels. In this case, it is preferred (for reasons that we will discuss later in the course) to code the levels as shown in the last two columns of the table below, designated by Xı and X2. Y SODIUM ΤΙME Xi X2 HYDROXIDE 5.95 3 30 -1 5.60 3 60 -1 5.44 3 90 -1 1 6.22 9. 30 -1 5.85 9 60 5.61 9. 90 1 8.36 15 30 1 -1 7.30 15 60 1 6.43 15 90 1 1 a. Using the variables Y, X1 and X2 (not actual time and sodium hydroxide! You will see why later!), fit the following multiple linear regression model to the data: (Model A) Y = (b0) + (b1) X1 + (b2) X2; subsequently, estimate the parameters and examine the residual plot (residuals vs Y hat). What does this residual plot…
You estimated a regression with the following output. Source | SS df MS Number of obs = 248 -------------+---------------------------------- F(1, 246) > 99999.00 Model | 1.2864e+09 1 1.2864e+09 Prob > F = 0.0000 Residual | 980713.166 246 3986.63889 R-squared = 0.9992 -------------+---------------------------------- Adj R-squared = 0.9992 Total | 1.2874e+09 247 5212005.66 Root MSE = 63.14 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 38.34444 .0675026 568.04 0.000 38.21148 38.4774 _cons | 49.99803 5.986441 8.35 0.000 38.20681 61.78925…
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920X2 (a) Interpret b₁ in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a…
2. You estimated a regression with the following output. Source | SS df MS Number of obs = 332 -------------+---------------------------------- F(1, 330) = 2.32 Model | 71599.1822 1 71599.1822 Prob > F = 0.1284 Residual | 10170207.7 330 30818.8111 R-squared = 0.0070 -------------+---------------------------------- Adj R-squared = 0.0040 Total | 10241806.9 331 30942.0147 Root MSE = 175.55 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .7575183 .4969893 1.52 0.128 -.2201484 1.735185 _cons | 28.87757 42.80371 0.67 0.500 -55.32498 113.0801…
Regression (1) in Table 1 estimates the effect of additional educationby regressing ln (W age) on Exp, Exp2, W ks, Ed and all the dummyvariables listed above. Does the estimated regression suggest that additional years of schooling increases the wage?
4. (2) Using data from 1950 to 1996 (N = 47 observations) the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated as YIELD, = 0.1717+0.01117t+0.05238Rain, (se) (0.1537) (0.00262) (0.01367) ... Where YIELD, is wheat yield in tonnes per hectare in year t; t =1, 2, . 47 is a trend variable to capture technolo change, and RAIN, is total rainfall in inches from May to October (the growing season) in year t. a) Interpret the coefficient estimates of t and Rain. b) Using a 5% significance level, test the null hypothesis that technological changes increase mean yield by 0.01 tonnes per hectare against the one-tailed alternative H₁ : ₂ >0.01. c) Using a 5% significance level, test the null hypothesis that an extra inch of rainfall increases mean yield by 0.03 tonnes per hectare against the one-tailed alternative H₁ : B3 > 0.03. d) Adding the square of rainfall to the equation yields YIELD, = -0.6759+0.011671t+0.2229 Rain, -0.008155 Rain? (se)…
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