Let T1 and T2 be random times for a company to complete two steps in a certain process. Say T1 and T2 are measured in days and they have the joint pdf that is uniform over the space f T1, T2(t1,t2) = 1 / 20 1 < t1 < 10, 2 < t2 < 6, t1 + 2t2 < 14. a. Sketch the space of T1 and T2 and shade the area where t1 + 2t2 < 14 b. Now shade the area where T1 + T2 > 10. c. What is P(T1 + T2 > 10)?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What is the radius of a circle with an area of 78.5 cubic inches? use 3.14 for pie

The probability that a u.s. resident has traveled to canada is 0.18 and to mexico is 0.09. a. if traveling to canada and traveling to mexico are independent events, what is the probability that a randomly-selected person has traveled to both? (page 109 in the book may ) b. it turns out that only 4% of u.s. residents have traveled to both countries. comparing this with your answer to part a, are the events independent? explain why or why not. (page 119 may ) c. using the %’s given, make a venn diagram to display this information. (don’t use your answer to part a.) d. using the conditional probability formula (page 114 in the book) and the %’s given, find the probability that a randomly-selected person has traveled to canada, if we know they have traveled to mexico.