Let the sample space be the two-dimensional plane. For any real number x , let Ax be the subset of the plane that consists of all points of the vertical line through the point (x,0) , i. e., Ax={(x, y):y∈Re} . a) Do the axioms of probability theory imply that the probability of the union of the sets Ax (which is the whole plane) is equal to the sum of the probabilities P(Ax) ?

The chart below shows the distribution of weeds in yard

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

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?