27. Discuss the effect of change of origin and scale on the moment generating function.

(3.) A system contains components connected in parallel as shown in the diagram. If all components operate inderentently, & each component has probability 0.45 of failing What is the minimum number of components that must be connected in parallel so that th Probability that the system operateds exceeds 0.9999? The minimun number of components that must be connected in parallel is.

Answer

5. The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 10 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 6 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of f in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.