A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and σ, 2² = V(X;), suppose that the mean values and standard deviations are as follows: = 230 M1 °₁ = 11 M2 = 260 Из = 150 02 = 13 7 03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume expected value variance ft³ ft6 = 27X1 + 125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain. ○ The expected value would be correct, but the variance would not be correct. Neither the expected value nor the variance would be correct. Both the expected value and the variance would be correct. The expected value would not be correct, but the variance would be correct.

The variable X, is the carbon monoxide concentration in air, and ten measurements are obtained as follows: 10.25, 10.37, 10.66, 10.47, 10.56, 10.22, 10.44, 10.38, 10.63, 10.40 mg/m3 . (i) Test whether the mean concentration of carbon monoxide in air is 10.00 mg/m3 . (ii) Calculate the power of the above test if the mean concentration of carbon monoxide in the alternative hypothesis is assumed to be 10.75mg/m3 .

please solve a and b.

The risk of a person developing heart disease is correlated with their BMI (or body mass index), which is calculated by dividing their body mass by their height (high BMIS typically mean the person is overweight). Heart disease is also related to a person's level of activity. Suppose a person's BMI is x and their physical activity is y (measured, for example, in minutes of exercise each day). Let h be a heart disease risk index (high values of h mean high risk of heart disease, low values of h mean a low risk of heart disease). h depends on x and y, that is, h3h(x,y). A simple linear model that only takes into account the effects of BMI and activity is (a) Would you expect a > 0 or a < 0? What about b? You would expect a 7o and b 0. (b) To fit the values of a and b, consider the following data. A patient with BMI of 15, and who does 50 min of activity each day, has risk index h = 150. A patient with BMI of 30, and who does 30 min of activity each day, has risk index h = 405. Use these…