Find the conditional probability mass function pY|X (y | 3).
1. Refer to Exercise 12. a. Let Z = X + Y represent the total number of repairs needed. b. Find µZ . c. Find σZ . d. Find P(Z = 2). 2. Refer to Exercise 12. Assume that the cost of an engine repair is $50, and the cost of a transmission repair […]
Estimate f, and find the uncertainty in the estimate.
1. The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p + 1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 […]
Estimate M and find the uncertainty in the estimate.
1. The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3 , L = 1.2 ± 0.1 cm, and A = […]
Estimate y, and find the uncertainty in the estimate.
1. Refer to Exercise 12 in Section 3.2. Assume that τ0 = 50 ± 1 MPa, w = 1.2 ± 0.1 mm, and k = 0.29 ± 0.05 mm−1 . a. Estimate τ, and find the uncertainty in the estimate. b. Which would provide the greatest reduction in the uncertainty in τ: reducing the uncertainty […]
Estimate v, and find the uncertainty in the estimate.
1. The resistance R (in ohms) of a cylindrical conductor is given by R = kl/d 2 , where l is the length, d is the diameter, and k is a constant of proportionality. Assume that l = 14.0 ± 0.1 cm and d = 4.4 ± 0.1 cm. a. Estimate R, and find the […]