. When a basketball player makes a shot, then he/she tries a harder shot the next time and hits (H) with probability 0.4, misses (M) with probability 0.6. When he/she misses he/she is more conservative the next time and hits (H) with probability 0.7, misses (M) with probability 0.3. (a) Write the transition probability for the two state Markov chain with state space S

Julia chooses a card at random from her set of cards. what is the probability that the card is labeled cat or hamster?

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?

What is the average rate of change for this function for the interval from x=2 to x=4 ?