Agame has 3 possible outcomes, with probabilities p 1, p 2, and p 3. the amount of money that you will win or lose for each outcome is v 1, v 2, and v 3, respectively. what is the expression p 1 v 1 + p 2 v 2 + p 3 v 3 equal to? the total amount you will win (or lose) in the long run. the average amount you will win (or lose) per game in the long run. the exact amount you will win (or lose) per game. the amount that you will win (or lose) for 3 games.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

How many verticies does a triangular prims have

How to do a maths question? i have a mock