Consider the parametrized 2-manifold X: [1, 3] [0, 2) R4, X(s, t) = ( s cost, 4 s sin t, s sin t, 4 s cost). Find X x 2 2 + x 2 4 dx1 dx3 2x 2 1 + 2x 2 3 dx2 dx4.

Chapter 18 Definitions Probability model- all possible outcomes Ex. If you toss a coin 3 times. What is the chance it lands on tails (2^3=8) ANSWER: 8 Sample space - unique outcome Ex. When tossing a coin a unique outcome would be either heads or tails. Sample space= head (H) Tails (T) Event - collection of outcome Probability Rules Rule 1 : probability must be a number between 0 and 1 Rule 2: all possible outcome must = 1 *if it passes both rules 1&2 it’s legitimate Rule 3 AKA compliment rule: if the question ask what is the probability that the event doesn’t occur Use this Formula: 1 - probability the event WILL Occur Probability = numerical (has to be a number) Ex. Probability of dog losing the race is .40, what is th