A mass-production line manufactures electrical heating elements with lifespans X; which have independent exponential distributions with pdf S(z.) = e X; > 0. exp 2

Suppose we ran logistic regression twice, once with 2 = 0, and once with 1 = 2. We .65 (102.09) and 0 = (00). Which value of 0 corresponds got the parameters 0 = (* to λ-0? Explain. 37.26 1.29

4. Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at – e-ßt C(t) В — а where a and B are constants with ß > a > 0. (a) occurs. (Your argument must use the first derivative test.) Using the first derivative test, find when the maximum concentration (b) (Your answer should be supported by a rigorous argument.) When does the rate of change of concentration begin to increase?

A regression function used to examine the factors affecting the chief executive officer salary in financial, manufacturing, utilities and transportation sector is given as below. Figures in parentheses are standard errors. Ln Y = 4.59 +0.257 log(X) + 0.158 D₁ +0.181D21 -0.283D31 se = (0.30) (0.032) (0.089) (0.085) (0.099) n = 209, R² = 0.357 Where Y = salary (in thousands) X₁ = annual sales D₁- D₂= D₂= (1, financial sector otherwise lo, manufacturing sector otherwise utililities sector otherwise Interpret the coefficient for D₂ Compute the approximate percentage difference in estimated salary between the utilities and transportation sector, holding annual sales fixed. Is the difference statistically significant at 1% level?