Tumor count comparisons: Reconsider the tumor count data in Exercise 3.3: a) For the prior distribution given in part a) of that exercise, obtain Pr(θB < θA|yA, yB) via Monte Carlo sampling. b) For a range of values of n0, obtain Pr(θB < θA|yA, yB) for θA ∼ gamma(120, 10) and θB ∼ gamma(12×n0, n0). Describe how sensitive the conclusions about the event {θB < θA} are to the prior distribution on θB. c) Repeat parts a) and b), replacing the event {θB < θA} with the event {Y˜B < Y˜A}, where Y˜A and Y˜B are samples from the posterior predictive distribution.

An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of 64 gallons per minute while flying through rain clouds. let c represent the number of minutes the plane can fly through clear skies and r represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 56c+64r < 900056c+64r< 9000 according to the inequality, at what rate does the airplane consume fuel while flying through clear skies, and how much fuel does it have before takeoff? the airplane consumes fuel at a rate of gallons per minute while flying through clear skies, and it has gallons of fuel before takeoff. does the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds?

The length of a shadow of the building is 36m. the length of the pole, which is perpendicular to the ground, is 1.9m. the length of the pole's shadow is 1.52m. what is the height of the building?

Angles r and s are complementary. the measure of angle r is 31 degrees. which equation can be used to find angle s?