Jill arrives at a restaurant at 6PM and waits for her three friends Moe, Agnes, and Dorothy. Each one of her friends arrives independently at a time uniformly distributed between 6PM and 7PM. (a) Find the expected value of the time at which Moe arrives. (b) Find the PDF of the time T at which ALL three friends have arrived. (Hint: find the CDF of T and use independence of the arrivals). (c) Find the probability that Jill has to wait more than half an hour by herself. (d) Find the PDF of T given that Moe arrives at 6:20 and Agnes arrives at 6:40.

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 solution to the equation e3x=12? round your answer to the nearest hundredth

Ashley spent half of her lunch money on a turkey sandwich. then she spent two-thirds of the money she had left on a bottle of juice and the rest of the money on a cookie. if the cookie cost $.75, how much lunch money did ashley have to start with?