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 […]