Need help with these questions.

Question 1. Determine which of the following random variables are discrete, and which are continu ous. Explain your reasoning. a) The number of moves required to lose a game of chess against world champion Magnus Carlsen. b) The height in meters of a randomly selected coastal redwood c) The balance of your bank account on a randomly selected day Question 2. Let X be a Bernoulli random variable with success probability a a) Compute IE(032) (the 2nd centred moment of X). b) Show that V(x) = a(1 a). 0) Compute the 10th centred moment of X. Question 3. The time X that it takes a lab assistant to nish a certain experiment has pdf a) Determine the value of k. b) What is the probability that it takes the lab assistant more than 12 minutes to complete the experiment? 0) What is the probability that it takes the lab assistant between 12.5 and 17.5 minutes to complete the task